As far as basic skills go, every character of a given class in WoW is the same (assuming they bothered to train all their skills; I've certainly left Feedback on my Priest and Wound Poison on my Rogue well alone). Where character customization comes in is with talents and gear. Gear is relatively easily switched -- many classes carry multiple sets routinely, and mods like ItemRack or Outfitter are great at helping you switch between them. Talents, on the other hand, are not quite so easy to switch up. Not only do you have to trek back into Azeroth to a major city to find a trainer, but you also have to pay, and of course the more you respec the more it costs. Granted, even the 50g maximum cost is a lot less now than it used to be, due to inflation, but it certainly adds up, and it's not really attractive to pay 100g (respec away, then respec back) just for one night of instances, PvP, grinding, or what have you. Blizz have said that the respec cost is not going away, as they want talents to have some kind of lasting implications, to be a somewhat weighty choice, but it does get somewhat frustrating to have to gimp yourself in one part of the game to be great at another part.
Tobold's MMORPG Blog is always a good read, and today he debuts a new column about "single features that I think are easy enough to implement and which could make World of Warcraft a much better game." This being WoW, I'm sure the idea has arisen before, but this week Tobold has come up with the idea of letting everyone have two specs and be able to switch between them for free. You could still charge to change either spec, on the same plan as before. To avoid on-the-fly spec switching abuse, you could make people go to a trainer to switch. If this were implemented, I'd also want to see a spec switcher NPC in Shattrath, because that's where the party is these days.