Old games, and those that are meant to emulate them, have partially or totally random character generation. You might not get the character you were hoping for. Hell, at least D&D let you pick your starting class (well, from those that you qualified for)... Warhammer Fantasy Roleplay forced players to roll their starting career.
I like random character generation. I think random character generation forces people to step outside their comfort zone. Among the more modern games that allow for near or total customization of the character, many folks I've played with over the years have an unfortunate tendency to simply make the same type of character over and over again. Joe always plays a magic-user, or whatever is closest in the setting. (A huckster in Deadlands, a psychic in a sci-fi game, a Tremere in old Vampire, etc.) Bob always plays high strength melee characters with bottomed out social attributes, etc.
Some of the most fun my gaming group has had has been when we do a one-shot with pregenerated characters, and the GM either randomly passes out characters, or chooses a character that is nothing like the type that the player usually plays. We've done this for World of Darkness and for Little Fears. The guy who usually plays melee monsters ended up playing a pre-teen beauty pageant contestant with a southern accent. The guy who hates Harry Potter ended up playing a sixth grader obsessed with Harry Potter. Everyone absolutely *loved* it. Yet, some of these players balk at the notion of a character created with an element of randomness to them. Hmmm.
In a previous entry, I said that I was defining old school gaming as gaming without an agenda. I think that randomized character creation reinforces that idea; you are making a character to play the game, not an alter-ego or an idealized self or whatnot. When you make a D&D or WFRP or Traveller character, you never know what you're going to get, Forrest Gump style. With more modern games, you usually get a point distribution system of some sort and are generally allowed to pick whatever you want. In fact, many games published in the last two decades have the player come up with a concept as the beginning step in the creation process. The player then picks precisely what they want within the limits of the resources (character points or whatever) I'm not sure where non-random character creation started, but it is now the order of the day. I'm not sure I can think of a currently published game that has random character generation, aside from the retro-clones, but I don't really count them because they are specifically emulating the game design and philosophy of Ye Olden Days. D&D, in its current incarnation, has dispensed entirely with random rolls for attributes, gold, and hit points. (Everyone gets a fixed number) Of course, random character creation has been dying a slow death in D&D for some time now. (4d6-L, arrange to taste, scrap if total attribute modifiers are below X...that was, in the end, hardly worth the random element at all)