It doesn't hurt, but it does not feel good either.
Basically it's just kind of uncomfortable, like going to the dentist. At the dentist they make you hold your mouth open and poke around with tools that pinch but do not hurt. At the gynecologist they put a speculum (a metal contraption that holds everything open for you) and poke around with a cotton swab that pinches but does not hurt.
The most uncomfortable part is when they insert the speculum, because it's cold and hard and does not have any give whatsoever. But again, it doesn't hurt, it's just uncomfortable.
It's cold because air will get into your vaginal canal, where air does not usually go.
Sometimes my doctor will also want to check my organs with her fingers, so after the speculum she shoves a hand up there. That doesn't feel so great either. lol. Basically she's feeling around to make sure everything is where it is supposed to be.
None of it feels anything like sex because it all completely bypasses any of the 'feel good' areas. It doesn't take very long, so after you're done you get to regain your dignity. =P