I like randomness, because I like to look at the abilities and decide what I want to do with that character. I'd rather pick the class and character concept to match the abilities than the other way round -- partly because it makes for a greater variety (how often would you choose to create a fighter with dexterity as the dump stat, for example?) and partly because I find more inspiration when I'm given something to start with. So my preference is for a purely random stat selection (typically 4d6, which I've decided is a reasonable power level, although back in the day I was quite the 3d6 purist). That means no rearrangement -- I want my dice to tell me which will be my good and bad abilities.
One interesting observation: the player (like me) who prefers more randomness than the campaign rules provide for has that choice, while the player who prefers point-buy when the DM's rules call for dice hasn't got the option. In fact, if I'm playing in a point-buy campaign, I'll generally roll ability scores, adjust them up or down 1 point to get the specified total, and if my rolled numbers are too far from the specified total I'll throw them out and roll again. For example, if I roll a 28-point character in a 30-point game, I'll change an 11 to a 12 and a 13 to a 14, but if I roll a 43-point character I'll start from scratch.
On the other hand, if I were DMing (hypothetical: I haven't DMed since 1/e), I'd set the standard rule according to my preference, but I'd be willing to accommodate players who come in with a more specific character idea than I generally start out with, so long as they weren't powergaming with it. For example, if a player really had some idea for a character he wanted to play, I might let him do what he wanted with a 28 point-buy, 28 chosen because it's just below the 4d6 average. Or if a player wanted a particular stat to be very high, but didn't care about the rest, I might let her designate an 18 in exchange for using only 3d6 for the rest of them. I don't think my players should have to conform to my own preferred character creation style if it doesn't suit them.