In racing, the pit crew is the group of people that makes sure that the racer can continue racing: They make sure that the car is maintained, that the racer is fed, and that the racer never gives up. Without the pit crew, the racer might do well for a good part of the race, but can't possibly last the entire length without a pit crew.
The pit crew are a step up from your flavor characters. These are characters that do important things, and not just help define your setting. These characters are the ones that not only provide a service for the main character(s), but also act as occasional confidante, friend, and even lover.
Consider Alfred Pennyworth. Alfred not only helps define Batman's world (Bruce Wayne is rich, so of course he has a butler), he also makes sure that equipment works, deflects the occasional noseybody, and even helps Batman do research. He has also acted as Batman's conscience, and has been one of the few people that has stood up to Batman and told him off. Alfred is probably as close to an uncle as Batman has ever had.
Commissioner Gordon is also an interesting supporting character. Besides giving Batman a somewhat legitimate official backing (Batman has been deputized more than a few times), as well as access to some information that even the Batman has access to, Commissioner Gordon has also stood up to Batman (yes, it can be done!), as well as provided some plot hooks and a friend to Batman.
How about Mary Jane Watson? Peter Parker needs someone to keep him grounded; you can't go up against one of the nastiest rogue galleries in all of comicdom without having someone ground you. Mary Jane may not have many contacts, may not have any powers, and may be one of the weakest wives ever, but she does something that no other wife in the comics can do: She keeps one of the most average heroes average. And that's no small accomplishment when you realize that Spider-Man has arguably one of the most eclectic rogues gallery of any established hero (it includes psycopaths, heroes, shape-changers, magical beings, and true multiple personalities).
May as well through Lex Luthor into the mix (ever notice how many double-L's there are in Superman's life [Lana Lang, Lois Lane, Lex Luther, Lara-El]?). An unlikely supporting character if there was one, Lex has shown the weaknesses in Supes, as well as his strengths. By taking one of the most mercenary personalities ever and adding in ambition and a megalomania that knows no bounds, Lex acts as Supes' best foil; because he adds so much to Superman, it's hard to imagine Superman without his dark shadow. It's because of how tied the two of them are, as well as how much The Businessman defines the Boy Scout, that Lex is more of a supporting character than arch-villain.
In short, a supporting character can add another dimension to your character by allowing him to be human. They allow him to mess up, and be called on it. They become just as vital to our perception to the character as what they wear, do, or say, and even become our friends and examples of what we can do (I wonder how many police chiefs have modeled themselves on Jim Gordon or businessman wish they could be Lex?). They show that the hero has someone to hang with, and just be human (or as human as some of these people get!). Ultimately, they represent aspects of the character that they support, and in such a way that we gain some measure of respect for both.
Sort of makes for an interesting pit crew. Mary Jane Watson may look gorgeous in coveralls (of course, she could look gorgeous in a burlap sac), and Alfred and Gordon might find it a change of pace, but I would not mess with a pit crew that had someone as vicious as Lex Luthor. How could you lose with a crew like that?
And that's sort of the point...