Officially, I use point buy. In practice, that ends up being to start with the standard array and tweak based on point buy costs. For most games, whether "serious" role-play or beer-and-pretzels, I prefer to use points to keep PCs balanced. While I've run very unbalanced games that have worked, as a general rule it sucks to be overshadowed on a regular basis.
If I were to run a more meat-grinder campaign (Tomb of Horrors or numerous others), I'd probably lean towards some randomized method. Some character death, even for uber-mench characters is part of that style of game, so it all evens out in the end. Trying to make the best of a bad role can be part of the fun. Also worth noting is that I'd probably just go ahead and use 1E rules for this style of game. I think the stat prerequisites for various classes also enhances that sort of game. But... that's not the typical game I tend to run.
I've really grown to dislike random generation, in most cases, because it doesn't do what it promises (IMO). To be "balanced" or "fair", random stats offer great reward, but great risk. In theory, you could get all 18s, but you could also end up with all 3s (depending on exact methods), with most characters averaged around some value (10.5, by 3d6). In practice, no one actually wants to play the character that lets the "cool" characters average out. So, lousy characters are generally allowed re-dos, which blows away the implied average. In some (most?) cases, it really turns into a contest to see who can whine at the DM best. Ick.
Some of the alternate methods discussed in this thread seem to put "appropriate" (very subjective) boundaries on the results, which works for me. My real problem with random generation is that I feel if you want to reap the rewards, you should endure the burdens, as well. In other words, "If you live by the sword...." Most groups don't do that.
