I'll list a few popular freeP2P programs i have personally tried and share my thoughts about each.
Vuze - I have found that Vuze is very good for video downloads and sharing and has some very nice features over other similar programs.
First of all you can stream movies and music to your PS3, Xbox360, psp, ipad, ipod, iphone and tivo. You can simply drag the video from your library in vuze to the devices tab to whatever device you happen to have connected to your network. I have only tried the PS3 because its what i have and use. It has worked out extremely well so far and i can even stream bluray quality dvds!
It also has a tab for burning DVD's. You just drag and drop the file you want to put on the dvd, follow the steps and burn. It really is that simple. This has quickly become my favorite program for video content.
The best way to find out is to download it and try it yourself. Its fun to play around with and has a lot of cool features. Give it a try! Vuze.com
Limewire- I'm sure you have all heard of this one as it probably the most popular P2P program out there right now. It is still the one i prefer for all of my music downloads. Vuze wasn't that great for finding music, but Limewire is. I think limewire is just the opposite of Vuze really. You usually get crappy quality videos from Limewire, but Vuze has a very large selection of all different formats and they are usually good quality. Its pretty simple to navigate and usually has almost every artist you can think of, but because it is a P2P program you aren't going to find all of them. Again, the best way to find out if it is good or not is to really try it out for yourself. Limewire.com
Frostwire - This is another one i've found floating around on the net and it seems to be very popular. It is supposed to be the equivalent of Limewire Pro which you have to pay for. I haven't really tried this one out, but it seems to look like a good one to try.