The one that springs immediately to mind is the Empire State Building. The main observation deck is on the 86th floor, which has 360 degree views over the city. There's also a smaller and fully enclosed observation deck on the 102nd floor; apparently the view is better, but you're indoors. I think it misses something not being able to feel the wind and see out without the glass, but YMMV! Wikipedia has a panoramic photo of the view, so you can get an idea of what the view's like. Two downsides though - for the 86th floor only it's currently $23, and there are normally long queues to get in, get up and get down...
There used to be an observation deck on the 107th floor of the South World Trade Center, which was very popular for photos and seeing Manhattan with the stairs leading up to the roof deck which offered magnificent 360o view of New York City and quite a bit surrounding areas on a clear day. The roof deck didn't quite go to the edge of the building but didn't have support columns in the way as the internal one on 107th floor.
The new One World Trade Center will, once complete, have observation area on floors 100-102. In a bit over a year you'll be able to see the view from there once again.