Quoted from RichmanBri:My current apartment building may not be the most ideal for this. I certainly have a lot to consider before I make a move.
I'm currently in the same boat. I live on the second floor of an apartment, and sound seems to be pretty dampened laterally, but I'm told that it travels between floors, which is my worst case scenario. The neighbors next to me have kids, so I'm not too concerned about bothering them (as long as I'm considerate about it at night), but when I introduced myself to the little old lady that lives below me, she said that she could "hear everything. EVERYTHING" with a sly wink.
Yikes...
Anyway, I've heard a lot of good things about the acoustic matting and I think as long as you take some measures, and keep in mind that it may or may not be appropriate to play loudly at 2 am, it'll be okay. That's my plan, at least.