Considering that Raditz bears family connections to Goku, it's pretty strange that he just dies and disappears within hours of his arrival--less than six episodes in the anime, a few pages in the manga (the one DBZ manga I actually own is the Raditz fight... well, most of it... I forget if the whole thing is in that one book), and if we try to make sense of the time that passes in the story... it is well under a day between Raditz's arrival on Earth and his death.
So, what depth do we get with Raditz? It's brutally clear how different he is from Goku--all about the killing, the destruction, even willing to take out his brother and young nephew to prove how ruthless he is. But that's not all, is it? Raditz seems to care about the fact that he and "Kakarot" are of saiyan origin; he seems intent on convincing his brother that because they are both saiyans, they must follow the same path. Goku, however, doesn't care at all about his race or his heritage--he is his own person, and he isn't about to kill innocents just because some rich alien asked him to.
Then there are the similarities--but these similarities accent a few differences. For example, Raditz and Goku both have ridiculously big hair--but Raditz's is bigger and flows down his back. In early DB (first appearances) Goku spent a lot of time with minimal clothing; Raditz doesn't seem to wear anything but boots, underwear and chest armor... but Goku never went around in underwear and armor--it was all or nothing (unless weighted clothing comes into the picture), and he certainly didn't wear anything to protect himself in battle; and with Raditz, his exposed legs and arms accent his muscle tone and added to his status as a strong, barbaric killer. Naked Goku accented Goku's innocence and made for cutesy humor--quite the contrast! Goku's hair makes him look goofy--Raditz's hair makes him look like a warrior. Goku eats fiercely because he's a bottomless pit of energy... and it's always a mildly disturbing, though typically comical scene when we see him attack a meal. When we see Raditz eat, it's very cold and further accents the barbaric aspect--when Goku is out in the woods catching his own food, he makes it into a game. . . not so with Raditz.
What else does Raditz do? What purpose does he serve? He introduces Goku's heritage, introduces a race of enemies and sets up a plotline that will lead to a great many things--Nappa, Vegeta, even Freeza are all initiated by Raditz... and each of these is pivotal to the story as it unfolds. He also serves to provide a situation in which Gohan can show his hidden powers, and for Goku to be killed and thus receive the training necessary to save the day when it next needs saving...
But beyond plot mechanics, Raditz serves to show us many things. Goku was always different from his enemies in the past, but never had their relationship with him gone deeper than Tsuru Sen'nin's vengeful desires upon hearing of Goku's defeat of TaoPaipai, or Piccolo Daimao reincarnating himself to continue his fight with Goku... who only fought him because he was killing people. But with Raditz, it's all about Goku--Raditz quite literally comes to the door and tries to drag Goku into a life that is completely opposite of what he has become. We know that Goku isn't going to join him without question--but we are still shown many things along the way. We see that Piccolo can change; we see the possibility of rivals joining forces to face a common threat; we see that regardless of what Raditz may say about his family connection to Goku or their race, he is still just another threat, and he starts the trend of saiya(ji)n pride leading to defeat--though not so extreme as in later cases, Raditz completely underestimates Gohan and the power of Goku and Piccolo as a team. He is also surprised that Goku would sacrifice his life just to defeat one threat, whereas Raditz is willing to sacrifice his dignity to doop a good guy like Goku into releasing him from the jaws of death. Essentially, Raditz shows us that it doesn't matter who you're related to, what race you come from, or even how superior you are to the best--you'll still wind up meeting a dishonorable end if you walk the path of evil.
The fact that Raditz dies and disappears so quickly, even though he is a blood relation of the main character accents his main theme even further. So, he's Goku's brother. But that doesn't mean anything to Goku--he's still just an evil brute trying to spread destruction and force others to become someone they aren't because of something over which they have no power. And we know what Goku does to wanna-be serial killers... so Raditz's disappearance after his defeat follows the same theme as the entire Saiya(ji)n race: it doesn't matter who you're related to, what race you are, or what class you're from... you're still an individual, and your choices will shape your destiny.
... That said, more Raditz would have been awesome.
