Well, this is the weirdest case I've had. After a PC crash I restarted Second Life and... Couldn't load body part message appeared. And I don't see my own body. Changing is no option, because the game prevents me from doing that until the body parts would load. Which won't because of an unknown reason. Nothing yet helped... What to do, waargh?
P.S. Body parts were default...
P.P.S. It seems that other players see me al'right. And my other character wasn't affected in any way.
Solved it not without some help. In my case all that was needed was to clear cache (Edit->Prefs->Network->Clear Cache if someone isn't familiar with it) and reset the game afterwards.