Can we destroy NPC villages? Can we destroy abandoned places? Can we destroy dirt pillars in the sky?
1 As long as theres no sign on player activity around it, yes. 2. not if it was built by a player 3. yes as long as its not new (if you cant tell, dont worry)
What Mirr0rr said is correct. However, if there was ANY player activity whatsoever (missing crops, etc) you CANNOT destroy this. It must be a fresh NPC village you found. This prevents accidental griefing. If you're not sure it should be destroyed, IT PROBABLY SHOULDN'T BE!
Just to add a note. We have players that build things that look griefed. So just because something looks griefed and abandoned does not mean it is. The general rule is: If it is not yours. Don't touch.
On SMP6, in the frontier, I've created a village. This is a player created village. It's got signs identifying itself as Perriville. No griefing it please. I just finished rebuilding it from the last griefer.