Does Vegeta care for the Z fighters?

[Majin Jator]

He probably cares a bit for Goku's offsprings:
He fought alongside Gohan, and was saved by him. Goten is the best friend of his son (that's his main trait, really), and his loss would hurt Trunks, so there´s that. I also think that he accept them as the proper descendants of the saiyan race, and care for their survivality.

Maybe he has a little ammount of respect for Krillin or Piccolo, but that´s all.

Anyway,I believe that he wouldn't get a "rage outburst" for anyone besides Bulma, Trunks or Bra.

[sintzu]

I believe that he wouldn't get a "rage outburst" for anyone besides Bulma, Trunks or Bra.

I think he would for Goku, especially if he died protecting him.

[Cetra]

He definitely does care about Goku. Especially in GT. When he thought Goku was dead, Goku's name was what he screamed when attacking Super Yi Xing Long. Bulma, Trunks and Bra of course as well. I would not say he cares as much about the rest than he does cares about those who I mentioned. And that is normal. But I think as someone said, there is at least some sort of respect for them.

[MaxZ]

But if in a hypothetical scenario he was fighting a new villain alongside piccolo tien Yamcha and krillin. And then the villain killed those guys would Vegeta get a rage power up/new form?

On a scale of 1-10 how much has he grown to care for everyone?

I'd imagine Tien/chaozu would be lowest considering those guys didn't even bother seeing their best friends over the 7 year gap between cell and buu.

Do we think Vegeta saw the likes of Krillin and Yamcha over that 7 year gap? (Yamcha lives at capsule Corp doesn't he?)

I think Vegeta probably saw Krillin plenty of times during that gap. It's loosely implied Krillin and 18 visit Bulma fairly often.

I have no idea about Yamcha though.

[Marco Polo]

I bet Vegeta avoids 18 as much as he can because of the possible awkward interactions (Vegeta is proud and 18 is one of the few people who unquestionably beat the crap out of him).

[Akira]

To varying degrees, I would say yes. Although he would never come out and say it directly, or ever let them think as much, a few of the cast have earned a measure of his respect. You really have to look back at his individual interactions with various characters and somewhat "read between the lines" to gauge how much or how little regard he has for any of them, but there are subtle hints. Before I go into my assumptions on the matter, I will state that it is very subjective and open to personal interpretation of course. (These assumptions also assume current point in DB Super, as I am certain he cared much less earlier on, but I will be referencing earlier points for context.)

Bulma/Trunks > Of course he cares about them, they are his family. There is no doubt on these two. He raged when Bulma was slapped, and he definitely cares about Trunks, he made sure he kept good on the promise to take him to the amusement park from way back.

Goku > He's gone from looking down on him, to hating him, to envying him, to yeah, all the stuff that happened in Z. Now, they maintain the facade, but they are allies and friends now. The bickering and verbal remarks are just how good buddies verbally jab at each other all the time. They are friendly rivals, trying to one up each other still, but on much less threatening, less deadly terms. Vegeta respects Goku as a warrior, but still thinks he's a goofball, and it gets under his skin sometimes.

Gohan > Vegeta never seemed to hold any serious animosity towards Gohan. Vegeta was a jerk to him when Gohan was a kid, but for a time, he was the only other saiyan still around. I think he is disappointed in him somewhat, but he still believes Gohan has enormous potential. Gohan saved Vegeta from being killed by Recoome, and Vegeta saved Gohan from being killed by Freeza. Vegeta also stepped in to distract Cell long enough for Gohan to deliver an overpowering blow when all seemed lost. Vegeta also apologized to him before leaving after that fight. There is a mutual respect there, and Vegeta clearly holds Gohan in a higher regard than many of the other characters.

Goten > When he knocked out Trunks before fighting Buu alone, he also knocked out Goten and made sure Piccolo took them both to safety. Goten is another member of the remnant saiyan race, and he cares about him in that regard. I'm certain he would fight to protect him if the need came up.

Chi-Chi > There is a certain level of positive regard here that I don't think has been mentioned. This is one of the only characters that Vegeta will tolerate criticizing or disagreeing with him and not lash out in response. They seem to be on the same page sometimes in regards to Goku's actions at times, so if anything they have that as common ground.

Piccolo > While constantly at odds with each other in years past, they seem to get along now. Vegeta entrusted Piccolo with taking his son and Goten to safety before his self sacrifice against Buu, and will converse with Piccolo when watching others fight. There may be a bit of a sore point on Vegeta forcing Piccolo to stand down during the recent tournament, but I think Vegeta was pissed at Frost, and it was more of a wanting to wreck any member of Freeza's race that would scheme and cheat than it was meant to be a sleight against Piccolo.

Dr. Briefs > There is definitely respect for the tech and brilliance of his work. Oddly enough, as early as the end of the Freeza arc, when Vegeta first went to Capsule Corporation to stay, he seemed to get along with Dr. Brief and like the guy in his own way. Dr. Briefs would explain how stuff worked, and Vegeta would listen, comment, and ask questions. I guess it may be an extension of having scientist type guys who did his bidding during his time in Freeza's empire, but he surely respects the guy, even if he doesn't verbalize it. However odd it may seem, Vegeta just "clicks" with his father in law.

Yamcha > The butt of Vegeta's jokes, and ex boyfriend of his wife in her younger days. I don't think at this point Vegeta is extremely harsh or mean to Yamcha anymore, but I doubt he cares much for him either. Doesn't seem to me he'd go out of his way to help him in any way, but I doubt he'd do much to bother him anymore either. I think it is just indifference. Probably at this point just viewed as "One of Kakkarot's friends, whatever."

Tenshinhan > Still hates Vegeta, still expects the worst from him. Vegeta more or less treats him as beneath his notice or care now. The hate is mostly one-sided from Ten towards Vegeta. I don't think Vegeta gives a damn about him, and wouldn't lift a finger to help him. Another "One of Kakkarot's friends" scenario.

Roshi > Roshi seems to like Vegeta somewhat, but I doubt Vegeta has an opinion of him one way or another. Vegeta might help him out of a jam if the situation came up, but I doubt they've ever really talked much or anything.

Krillin > Of all the human fighters, Krillin is probably the only one Vegeta has a decent respect for. He may make comments at Krillin's expense, but he's fought along side him, and they seem to get along to an extent. Krillin didn't hesitate to make the move to kill Vegeta at the end of the fight on earth in the saiyan saga. Krillin spared him only at Goku's request. Krillin killed all but one of the remaining saibamen in one attack, and nearly killed Nappa in one shot. Despite being weaker than saiyans, Vegeta definitely respects Krillin's strategic thinking, and probably holds him in moderate regard as a warrior despite being a mere human. In the ROF arc, he jumped in the way to protect Krillin so that he could safely get a senzu to Goku in time. The argument could be made that he did it for Goku and not for Krillin, but I think he likes the little guy a bit. They seem to have found their place where they get along well, and can even joke around..a little bit.

North Kaio > Seems to have a mutual respect with Vegeta now. They spoke with each other to make the plan for the Genki Dama against Buu, and North Kaio contacted Vegeta to warn him about Beerus. It is nothing like Goku's relationship with North Kaio, but in Goku's absense, Vegeta is his go to guy.

Everyone else is more or less "friends and family of Goku or Bulma", and tolerated. I don't think he especially cares for many of them, but I don't think he has any ill-will towards the rest either. Good question, interesting topic idea!

[sintzu]

Yamcha > Doesn't seem to me he'd go out of his way to help him in any way.

Tenshinhan > I don't think Vegeta gives a damn about him, and wouldn't lift a finger to help him.

I'm not sure about that, if someone had one of them by the neck and was going to blow their head off I doubt he'd just watch.

[Akira]

I see what you mean there, but I just meant he wouldn't care if those guys got stronger or not, wouldn't goad them about their training, or do anything out of his way to help them. (I didn't specify what I meant, so your conclusion was easy to draw.) Sure he'd probably save them from being killed (for Goku or Bulma's sake), but aside from that, I really don't think he gives a flip about those two.