Bring out the dead horse, it deserves another beating. I have noticed this is a pretty popular request in the forums, and for good reason.
A character almost always looks different in the game than in the generator.
Maybe it's the lighting in the generator, maybe it's the limited angles in the thing, but a character almost always looks different in the game itself. I spent hours making a perfect replica of myself in Fallout 3 only for me to come out in-game looking like somebody beat me in the face with a stick during my formative years. I tried making Red Sonya in Skyrim, and in the generator she was beautiful. In-game, her face looked like somebody dropped a ham down a flight of steps. It isn't just you, Zenimax (and Bethesda). I think this holds true for pretty much any game. I was recently playing another big-budget fantasy RPG from another studio and made a great looking elf with a big smile and bright eyes. She came out looking like she was wrung through a lemon squeezer, grumpy as hell. This isn't the only good reason for an appearance change, though...
Good roleplayers like to imagine their characters growing and changing as they play.
Maybe my Khajiit has grey hair and an eye patch by the time she's Veteran rank. Maybe my Bosmer got a tan. My sorcerer's been at the receiving end of so many danged inferno attacks that she probably deserves that "burned all over the face and body" option in the character generator. A good player gains an attachment to their characters and wants to watch them grow as they play. Being able to change a character's appearance allows us to immerse ourselves in this fashion. After saving Tamriel from the evil machinations of Malcolm McDowell, I'd like to venture into Cyrodiil with a mohawk and warpaint and go crazy on some people in PvP. I've earned it at that point. I can save the world, but I can't shave my head?
Please don't charge real money for it.
Seriously. We are already buying wedding dresses, lizard steeds, and hilarious little pets that do little except make us look totally awesome. We can probably all expect to buy at least one or two respectification scrolls in our lifetimes. I think this is basic enough that it should be implemented simply to prevent the "deleted and remade my character three times tonight and he still looks like Steve Buschemi" problem. I'm happy to keep giving Zenimax my money, because I am into their game pretty deep and intend to stay there for a long time. Giving us this one for "free" (IE not real-life money) would be a stellar gesture on their part.