Soulseek
Soulseek is a free filesharing program without any ads or spyware.
This software is mostly centred around music, but contains all the necessary features expected in a P2P program. This includes usernames and chatrooms and the ability to view a user's shared files. I really like the smart search bar that allows you to match exact terms, exclude terms, or incomplete phrases with using an asterisks before or after part of a phrase.
Soulseek also searches files that are offline. I think that since the userbase is small, the program author still wants users to know that your search results are out there, but may be offline at the moment. Offline search results are shown in a faded colour and the search can be saved for later.
On top being free from ads and spyware, the program allows you extra security by letting the user set the limit on the amount of downloads or uploads at a time. Additionally, you can limit the maximum amount of speed for both uploading and downloading. This is useful if you need to multitask on the Internet, and don't want filesharing to take up bandwidth on your line.
This is a small and basic program. There is no full built in media player. Clicking a finished file transfer will play the file, but the user will not have any controls like volume control or stop. I suggest getting a good media player in addition to this software.