To flesh out the title a bit more:
If you could remove one physiological aspect of being human, which one would you get rid of? Assume that your body would magically continue to function even without it.
For example, remove the need to eat. You don't have to come up with alternatives for how your body would gain nourishment, it just would, and eating would be optional. However you can only get rid of one thing, so under this example you would still (for some odd reason) have to defecate.
Personally, I'd get rid of the need to sleep. I spend nearly a third of my life sleeping, it would be great to reclaim all those hours.
Edit: Some clarifications. We're removing a single aspect or need of being human, and assuming the rest of your body continues to work as though the thing you removed was still happening under optimal conditions.
So if you remove breathing, you never have to inhale or exhale again. You can if you want, but your body works even if you don't. Through the magic of the MMO-C off-topic boards, your blood still gets magically oxygenated, and carbon waste magically disappears from it. You can go live underwater if you want. However you didn't grow gills, so if you suddenly breath in a bunch of water, your lungs aren't going to take kindly to it. If you inhale poison, it's going to mess you up.
Edit: For those responding with "mortality" and the like, assume it would only remove "death by aging". It's not invincibility, or immunity to sickness, and you would still suffer some effects of being around for a long time. For example, the long term effects of gravity on the body dragging everything down. Or the weakening of muscles that comes as a result of being physically inactive for years on end (if you are inactive).