Best moments for each character

[Baggie_Saiyan]

Goku- Looking dejected when King Kai offers him a lunch break
Vegeta- Use of his middle finger
Gohan- He has a few
Piccolo- Teaching fusion to Goten/Trunks
Kid Trunks- Getting Screwed at by Goku
Goten- Going SS for the first time
Future Trunks- The whole private talk thing with Goku
Krillin- His entrance in DB

[TheMightyOzaru]

Vegeta: Going SSJ or sacrificing himself.
Goku: Kicking Freeza's ass.
Gohan: Killing Cell with the Father-Son Kamehameha.
Piccolo: Surprising C-17 with his new power.
Mirai Trunks: Killing C-17 and C-18
Goten: Fusing with Trunks
Trunks: Knocking Goten out of the ring.
Krillin: Taunting Freeza.
Tenshinhan: Fending off Cell.
Yamcha: Dying.
Chaozu: Also dying.
Freeza: Toying with everyone
Cell: Being a creepy bastard and absorbing people.
Buu: Killing everyone on Earth in mere seconds.
C-18: Kissing Krillin
C-17: Toying with the Zetto Senshii
Gotenks: Commanding his Kamikaze Ghosts.
Gogeta: Killing Janenba
Vegetto: Kicking Buu's ass as a jawbreaker.

[Revolution]

Goku - holding on to Raditz to ensure his defeat even though it meant his own life was the price.. Protection for family and friends & beating Frieza so calmly and easily in the end.
Piccolo - taking Gohan to be trainer but keeping a watch on him.
Vegeta - his death at frieza's hands and his speech to Goku.
Gohan - Killing Cell.
Krillin - generally always stepping up to the plate despite nearly always being completely outclassed.
Tien - Stalling Semi-Perfect Cell.
Yamcha- His first fight with Goku.
Mr. Satan- Befriending Fat Buu.
Future Trunks - chopping up Frieza and defeating the androids in his timeline.

Minor characters:
Roshi - Blowing up the moon.
Bulma - creating the dragon radar or making time machine.
Yajirobe- Launching two sneak attacks on Vegeta and living to tell the tale.
Chiaotzu - commiting suicide to try and take out.. Nappa?

Villains:
King Piccolo - beating Goku so badly that his heart stops.
Vegeta - Getting right back up after being hit with both the x4 Kamehameha AND the Spirit Bomb, and proceeding to spend the rest of the fight kicking Goku in the ribs.
Freeza- His legendary beatdown of Vegeta, which ends with Vegeta crying "like a little bitch".
Cell- One-shotting Gohan, Trunks, and Vegeta in seconds, all without any effort at all, after becoming SUPER PERFECT.
Fat Buu- Annihilating Majin Vegeta.
Kid Buu- Beating the crap out of Goku and then mocking him by doing stupid dances. Either that or actually blowing up the Earth.
Super Buu-
-Base- The Human Extinction Attack.
-Buuccolo- Revealing exactly why he didn't regenerate his head tentacle...

I ripped a lot of that from a previous post because I agree with the bulk of it but I think it can be agreed that there are plenty of awesome moments all in all

[dbzfan7]

Goku: Going SSJ. Changed everything.

Gohan: Killing Cell. His best accomplishment.

Goten: Surprising Gohan with SSJ.

Vegeta: Sacrificing himself. His character takes a big turn there. That or the Number 1 speech.

Trunks: Going back to the future and kicking ass.

Kid Trunks: Surprising Vegeta with SSJ.

Vegetto: Making a fool out of Boo

Piccolo: Sacrificing himself for Gohan. Shows his new nature as being a good guy.

Tenshinhan: The whole confrontation with Tao Pai Pai.

Krillin: Get back to you on that.

Yamcha: Hitting Chi Chi. His greatest accomplishment by far.

Muten Roshi: MOON BUSTING.

Chaozu: The sacrifice I guess.

Tao Pai Pai: Beating Goku.

Freeza: Anytime he struck fear into people. (Unless it was Granny Fr(I)eza, Fuck Grany Fr(I)eza)

19: Making Vegeta look good.

20: Almost Killing Yamcha. (Yeah that's not much)

18: Breaking Vegeta's arm.

17: Demolishing all the warriors with 18.

16: His speech to Gohan

Cell: Being sneaky and conniving and avoiding everyone to get stronger only to come back and whoop Piccolo.

Fat Boo: Fighting Kid Boo

Super Boo: Turning one sided fight against Gohan into an almost guaranteed victory.

Kid Boo: Beating Goku/Blowing up Earth.

Mr. Satan: SAVING THE UNIVERSE

[Kid Buu]

Just doing Z Senshi for now:

Goku - Singing with Jackie Chun

Yamucha - Sodikan against Kami.

Master Roshi - Every moment

Krillin - Spamming the Discs at Freeza.

Tenshinan - Fending off Cell

Chiaotzu - Being really fucking creepy.

Yajirobe - Cutting off Vegeta's tail.

Piccolo - Dying for Gohan.

Vegeta - Majin Vegeta sacrifice.

Gohan - Saiyaman arc.

Trunks - Killing Mecha Freeza.

Kid Trunks - Winning the Budokai Tournament.

Goten - Pandora's Box fan comic.

[TheSeductiveTomato]

Vegeta - Slaughtering most of Frieza's henchmen/finally admitting Goku is stronger.
Krillin - Fight with Chiaotzu.
Piccolo - Killing off Cooler's henchmen.
Roshi - Standing up to King Piccolo and sacrificing himself.
Tien - Fights with Yamcha and Roshi/Jackie Chun.
Yamcha - I'm sure he's had some, but I can't think of them right now. :$
Yajirobe - Fight with Symbol.
Oolong - Ruining Pilaf's wish.

[Ajay]

Can't say I have a favourite moment for every character but I'll list a few standouts: -

Vegeta - I've always found his death scene on Namek particularly touching. It's our first real insight into the compassionate side of the character. We see him caring for his race and truly begging Goku at the risk of his pride. Horikawa's delivery is so point that it really brings that scene to life.

Of course, I can't forget his farewell to Trunks in the Buu arc. Such a heart wrenching and incredible moment for the character. Vegeta actually being selfless as he sacrifices himself for the good of the Earth?! Just brilliant.

Goku - There's very few moments with regards to Goku that really stand out for me in terms of his character. If there's one thing we can count on with Goku, it's that he'll always stay mostly the same. As a result, near enough all my moments revolve around battle moments.

It's gotta be the Kaioken against Vegeta. Nozawa's scream as she says the word is just magnificent! It's really her screams that sum up all my favourite moments as my next one is the first Super Saiyan transformation. A truly terrifying moment is uncertainty on a first viewing and forever an iconic scene within the franchise.

I do enjoy Goku's final goodbyes to everyone at the end of GT. That's certainly a standout that isn't battle related!

[Jackal puFF]

My favorite Chiaotzu moment was when he tried to steal Piccolo Daimao's wish.

Favorite one for Yamcha is definitely his fight with Kami. I'm still amazed by that Sokidan.

And now since BOG is out and about, Vegeta beating up Beers for a few seconds.

Roshi's fight with Tien!

[soulnova]

Goku... hold Raditz, first part of his fight with Nappa/Vegeta, his SSj transformation.
Gohan, fighting one on one with Vegeta, turning Oozaru against Vegeta, fighting Freeza, Gohan Sjj2 transformation.
Krillin cutting Freeza's tail, fleeing from him and *not dying*... until after the Genkidama.
Vegeta.... getting all of "Freeza's balls" after he got healed. Fighting Buu to make time for Kakarot. Most of the rest is him showing off and things going terribly wrong afterwards.
Piccoro... geez... everything?
Yamcha... Managed to stop Oozaru Goku.

[Revolution]

I don’t know at what at point this becomes my bumping a topic butttt I would like to revise and update my opinion on the subject a few years on...

Goku - His run across snakeway and when he showed up to the fight with Vegeta and Nappa. The beginning in some ways
Yamcha - Confirming that Trunks wasn’t indeed not his child.
Master Roshi - Any time he imparts wisdom of situation or person from long a go
Krillin - His consistent bravery against overwhelming odds, Frieza, Cell & Cell Juniors... it goes on
Tien - holding Cell off with the Tri Beam and Showing up to help against Buu despite certain death basically guaranteed.
Chiaotzu - Attacking Nappa
Yajirobe - Being carried with Bulma by Gohan.
Piccolo - Fusing with Nail and subsequent stand off with Frieza
Vegeta - Dying from Freeza's Attack on Namek and opening up to Goku.
GohanHis journey to become a Super Saiyan in HTC but mostly his ascension to Super Saiyan 2 and the fight that followed is still my favourite DB event. Bonus, the Golden Fighter.
Trunks (Android saga) - being a total surprise with his super Saiyan transformation to killing Frieza... just who was this guy and how strong must the Androids be??
Trunks (Goku Black) - His unknown transformation and the sword of hope Attack or spirit bomb sword.
Kid Trunks - Winning the World Martial Arts Tournament.
Goten - Turning Super Saiyan in front of Gohan.
Mr. Buu - His friendship with Mr Satan and helping the blind boy. Also, morphing his face to try and get a kiss.
Beerus - his dumbfounded outrage that Majin Buu had just had the nerve to eat all that delicious pudding right in front of him. Also him knocking Goku out no problem.
Whis - His whimsical ways and love of food. The moment that intrigued me the most was him taking care of Beerus with no effort.
Cell - a weird one cause it’s not good for the character but his denial and gradual realisation that Gohan would annihilate him. But also his cocky return taking out Trunks.
Frieza - His return to life and deciding to train and be more intelligent in his quest for vengeance, didn’t work out but.. Also in the namek saga showcases just why he was the most powerful before Goku’s ascension. Really felt the overwhelming odds with this villain.

I can’t think of more right now but I will update

[GodKaio-Ken]

Gohan - Awakening SSJ2 eblven though he fooled around and flubbed it up a bit. Its still one of the few moments I enjoyed his character.

Goku - I'm going old school. Nothing can top the will to win he showed against King Piccolo in the original DB. Ill always remember that one armed push to victory.

Tien - His original fight with Goku. Great battle. Honorable mention to holding back Cell.

Ill think of more later.

[Akyon]

Goku: When he turned up to fight the Saiyans. Just the way he fought Nappa was incredibly impressive at the time. Standing on Nappa's HEAD was hilarious and cool.

Gohan: Gathering his resolve and beating down Frieza after Krillin's 'death' at the hands of the second form transformation. That pure rage.

Vegeta: The Saiyan Saga showdown with Goku. Closely followed by him cunningly running rings around the Frieza force on Namek.

Piccolo: That fight with 17 is still one of my favourite battles in the whole dang series.

Krillin: Hard to choose as a Krillin fan. Krillin Vs. Goku? Krillin Vs. Chiaoutzu? Saving Gohan from Nappa? Saving Gohan from Frieza(with the added bonus of being the only one to do any kind of semi lasting damage)? Solid Snaking it up on Namek? Breaking all Recoome's teeth? Saving the young woman from Imperfect Cell? Sacrificing himself to fight Super Buu? Teaming up with 18 in the ToP to do that dodgeball ki attack? Ringing Gohan out in a test battle? Standing up to Piccolo in the tournament and causing the Namekian some concerns about how easy it will be to take over the planet? Killing all those Saibamen at once? Using his wish to make life better for the Android twins? List goes on.

Yamcha: Telling Trunks what Vegeta did after the latter died. An underrated nice moment that showed he held no grudges. Striking out Botamo and Cabba in the baseball episode with his superior sports skills is a very close second.

Tenshinhan: Anything before his redemption; His snarky comments when he was an antagonist were pretty enjoyable. Semiperfect Cell was still good though.

Chiaoutzu: Chiaoutzu Vs. Krillin was probably his best showing.

Master Roshi: Chun Vs. Tenshinhan. Whilst responsible for altering Tien's mindset, and taking away a lot of his villain snark as a result, this was the time I most enjoyed Roshi as a character; no perverted gags, just good old martial arts mentoring and guidance.

Yajirobe: Defeating Cymbol in half a heartbeat.

Bulma: Most of Super in all honesty. Her restoration of a time machine was pretty impressive.

Future Trunks: Spirit Sword. Screw you and your power level calculations; I liked him being the one to try and save the day.

Kid Trunks: Snapping his future self out of his depression.

Goten: "I'll avenge you father" when talking to the then dead Goku about Hit.

Chi-Chi: Chi-Chi chasing off the abusive home tutor who was whipping Gohan.

18: Trying to use the Dragonballs to wish for a present for her husband is probably the sweetest thing ever shown in this series.

17: Vs. Piccolo. Close second is his amazing dad joke to Marron.

Videl: Fighting crime pre-Gohan girlfriend status.

Mr. Satan: Kicking the ever loving crap out the guys who shot Bee. What a badass.

Frieza: "My hand slipped"

Cell: Smacking Mr. Satan away with a single backhand.

Buu: Vs. Basil.

Jaco: Taking down that alien frog fugitive AND getting Bulma the chance to see Zuno in one single action.

Beerus: Taking out Zamasu

Whis: Karate chopping Beerus.

[8000 Saiyan]

Goku: Going Super Saiyan for the first time.
Gohan: Going Super Saiyan 2
Vegeta: His number 1 speech.
Trunks: Killing Frieza, King Cold, the androids and Cell.
Piccolo: Sacrificing himself for Gohan.
Krillin: Marrying Android 18.
Tenshinhan: Using the Kikoho against Cell.
Yamcha: Cutting Great Ape Goku's tail.
Yajirobe: Kiling Cymbal.
Master Roshi: His battle against Goku.
Bulma: Marrying Vegeta.
Chi-Chi: Slapping Super Buu.
Frieza: His fight against the Zetto Senshi.
Cell: This: (https://www.youtube.com/watch?v=AD23hfGKZoY)
Buu: Standing up to Kid Buu,

[Revolution]

Secondary mentions..

Ginyu squad - fight on king kai’s Planet and just any moment they’ve done one of their signature poses
Bardock - Facing Frieza moments before Planet Vegeta was destroyed and his vision of Goku giving him some form of piece.
Broly - his blue hair stage of that transformation

[ABED]

Never mind that he easily could have used a kiai or his stretching abilities to move Gohan but Toriyama-sensei wanted destroy hope for reviving the dead.

What? The attack was already heading towards Gohan, so hitting Nappa wouldn't have done anything, it's doubtful his arm stretching ability is quicker than his legs, and a Kiai blast wouldn't have stopped Nappa's attack that was enough to kill Piccolo. I don't remember everything about the scene, but whom is Piccolo closer to?

Favorite moment for Kuririn - being the first to see Goku after the end of the 22nd Tenkaichi Budokai. It's a great moment of connection.
Piccolo - giving his life for Gohan
Vegeta - Either "You are no.1, Kakarotto!" or his battle in the Saiyan arc. He was so badass in that fight. He takes everything and keeps going, but it doesn't feel cheap nor does he just tank every blast.
Goku - winning the Tenkaichi Budokai or the catharsis of him killing Piccolo Daimao
Gohan - turning SS2. Yeah, it wasn't the most elegant way to get there, but it's still such a memorable moment.
Mr. Satan - Telling the world to give Goku their power. It was a beautiful climax to his arc. If he wasn't going to be revealed as a fraud, which would have been a great moment of justice, using his unearned fame to help save the world is the next best thing.
Yajirobe - saving Goku from falling to his death after he killed Piccolo Daimao.
Muten Roshi - stepping down in the 22nd Tenkaichi Budokai. He achieved his goal of teaching his students and he was satisfied that the next generation of warriors' time had finally arrived. It's capped off with him talking to Tenshinhan about walking down a better path.
Chaozu - his character is only interesting in the 22nd Budokai. He calls Kuririn "baldy" even though he has only one hair, and his moments of stupidity. Unfortunately, all that gets dropped when he becomes a good guy.

[RIPinPeaches]

Goku- His sacrifice against Cell or Goku meeting gohan during red ribbon army arc
Vegeta- swallowing his pride and helping Gohan by distracting Cell, resulting in Gohan's victory, death on planet Namek, Majin boo sacrifice
Gohan- SSJ2 transformation I just liked unmei no hi tamashii vs tammashii
Yamucha- beating suke (the invisible man)
Tenshinhan- the 22nd tenkaichi budokai at the very end when he beats Goku
Kuririn- Using the spirit bomb against vegeta
Muten Roshi- his fight against Goku in the 21st tenkaichi budokai
Chaozu- Him sacrificing himself against Nappa because Chaozu is the character I dislike the most
Piccolo- sacrifice for Gohan or his fight against freeza

[TheDragonBallGuy75]

Vegeta (To Supreme Kai) - "Spend most of your life ruled by another, watch your race dwindle to a handful, and then tell me, what has more meaning then your own strength?!!"

I realise that Funimation took some liberties with this line, but it did so much to justify Vegeta's anger towards Goku, and his relentless pursuit of power. Even at the cost of every joy that Earth could have offered him.

[Ripper 30]

The Best Moment for Vegeta is definitely the Respect Speech he gave for Goku in Fight Against Kid Boo, it showed how vegeta has Developed as an overall character and now he admits that goku is better than him and he was being blinded by his pride and all.