Yeah, it all depends what you're downloading. Like Trico said, public domain stuff is fine. People who put up their own stuff for free. Music under the major labels, movies, software that normally costs money (such as Dreamweaver or MS Office), that's all illegal here in the states. Using P2P software is perfectly legal, but using it for illegal purposes is not.
If you are getting the files then that would mean someone is distributing them. If someone is distributing them and it is not public domain then that means they are breaking the law. If you are obtaining files from someone who is breaking the law, then you are obtaining them illegally.
So to answer your question, things aside from music that are illegal to "fileshare" include Movies, certain files, ROMS and Emulators (unless you own the Cartridge/Console). Anything associated with the media is ususally illegaal to download! ^^
If you own the product, you own the copyright to it and that is any music, video, ect. Like I can take one of my store brought CD's, burn it onto my computer and then burn it to another CD, it's legal... cause I brought the CD itself... or some of the soundtracks I have on my computer... I have the game itself... so the music from the game is legal. It's a court case for the US back around the 70's when Tapes first came out... if you own the copyright orginial copy, you can do whatever you want to the product for yourself.