Grum's got some gems on this thread.
Obviously hair is what I would prefer to lose (I'm already losing it anyway. Hah), but as DD7 points out, that's just too easy. So of the remaining functions, I'd go with teeth. I'd probably prefer to lose a limb before I lost my sense of taste and smell. Food is just too important to me; if I lost my ability to appreciate it, that would be devastating.
The option to choose between two neurological/cognitive processes (deeper thinking/personality) is interesting. At face value, either of them seem to be the worst to lose IMO, but there's a lot of variables. Like, if I lost my deeper thinking abilities, would I understand what I was missing out on? Would I wish for the ability to laugh and cry and empathize but be unable to attain that? If so, that would obviously be the worst. But if it turned out that I were not aware of what I were missing, then the old adage,
ignorance is bliss would hold true.