I'm a big fan of random character generation. For one thing, I just love randomness. Modern gaming often seems to be a huge exercise in reducing its effects, and I find this trend boring. I want to be surprised by what the dice throw up, the more surprises the better. (This is probably why point-based systems like GURPS, or diceless games like Nobilis, have never been by thing.) And why should the character I'll be playing be any different?
D&D character generation in its 'purest' forms is nicely random, but only up to a point. Once you have your stats, the rest is up to you. Weirdly, D&D characters also arrive more or less fully formed into the universe; you start off with a blank piece of paper, roll 3d6 six times, and hey presto! a 50-year old elven druid appears from the ether. This is a strength of the system, because it's quick and easy, but it's also less fun than, say, Cyberpunk 2020 and Warhammer Fantasy Roleplay.
In Warhammer Fantasy Roleplay, random character generation extends far beyond generating stats. Not only can you roll on a 'starting career' table containing dozens of entries (from Pit Fighter to Zealot to Rat Catcher), you also randomly determine pretty much everything else, including eye colour, star sign, distinguishing features (like 'pox marks'), birthplace, family background and and finally even your name (plus names and careers for your family too, if you're so inclined). I love this process and can spend a considerable amount of time merrily churning out characters. It almost always throws up interesting plot hooks for the game, too: who was this pit fighter born in a hovel in Talabecland, why does he have a missing eyebrow, and what are his 5 sisters, one of whom is an outlaw, doing? Boom: loads of ideas for the GM to use in the game.
It wouldn't be hard to incorporate something like this into a D&D campaign, and in fact it's something I might try. In particular, I think such random tables are fantastic if you're going to be running a game in a non-standard (i.e. not high fantasy) setting: we all know how hard it is to get players to invest in a game set in ancient Akkadia or whatever and how likely they are to come up with stuff that just doesn't fit. How much easier is the process made if you can randomly generate a character using tables that are tailor-made to produce results that fit in with the setting? At a stroke some of the key difficulties running campaigns in Tekumel, Athas or your bizarre homebrew setting are removed.
Of course, the best random character generator of all was Cyberpunk 2020's, with its silly life path and life history tables which never failed to turn up weird and wonderful results. ("I'm playing a Fijian netrunner who likes wearing fingerless gloves but otherwise goes around completely nude, whose favourite possession is a childhood toy, and who has five sworn enemies, seven ex-lovers and grew up in a pirate gang? Cool.")