Class is Role

What Roles does your game support?
White Box introduced the world to this thing we call tabletop role-playing or adventure gaming. White Box uses class to define role in the game. Obviously the roles White Box supports are fighting man, magic user and cleric. If you add Supplement I Greyhawk the additional class and role of thief and the subclass of paladin become available for play. The class system is an easy way to define what roles are expected to play an important part in the type of story that unfolds. Class defines the movers and shakers in the imaginary world and helps the payer know how they fit into the game.
Other games have followed White Box and many use the class system. Each game using the class system provides a similar structure for role-playing even though the classes may differ greatly. Popular early classes that went beyond the White Box three include alchemist, forester and beast master. Inclusion of these roles as player character classes helps to define the type of game likely to be played. In my experience the addition of the thief class has the greatest single effect on White Box and similar systems because it brings into the game a skill system and defines sneaking and stealing as something the game can be about. A campaign based around a thieves guild where everyone plays a thief is probably quite different from one where there are no thief PCs.
It wasn't too long after the White Box taught people about this new hobby of role-playing before a class-less system was created. PCs who are rolled-up or built on a point-buy system without class in the equation allow for virtually any role to be played as a PC. I think it is even more important in a classless system for the referee to have input on the PC make-up because they PCs really shape what the campaign is going to be about. I like several systems that have billed themselves as class-less, but they run the danger of becoming a one-class system if everyone optimizes their PC to the same standard producing virtually the same skill-set. It is easy to end up with everyone playing the same "adventurer" class character.
One of the advantages of White Box was the three classes each had their own strengths and weaknesses, each had a role to play in the adventure that unfolded during play. For some players this seems more important than others. The 4h Edition rules retained traditional class names like fighter and magic user, but redefined roles as Defender, Striker, Controller, etc. I think this is informative and can help players understand the role they are playing in the game while allowing some diversity among the Strikers, etc. so that not all PCs built as Strikers are the same. For some players diversity is more important than others.
I have found diversity can be the background, character and personality I bring to any "generic" PC created with just about any minimal chargen system. There is really no reason for two White Box fighting men PCs to be played the same even though they may be mechanically the same. "Color", "personality", or other ways of describing unique features that may play no mechanical role in the system go beyond the role of class, but can be great fun. There is no better way to bring "life" into a campaign than by thinking of the PCs as "real" people with lives beyond the game. It isn't necessary to do this and many a fun game has been played with two-dimensional PCs. Whether one prefers their PC as simply their playing piece or "pawn" in the game or enjoys fleshing them out, the idea is for everyone to have a role to play in the game and to have fun. There is no "one right way" to do this.