Tor and JAP are probably the best services, and they’re free as well.
JAP is perhaps a little too good. That's why the German Police insisted in 2004 that a backdoor be put into the product to allow interception. As a result of court action, no backdoor was implemented at that time. The German government at one time ordered JAP to put in a backdoor to the program to catch a pervert even though it was against the law. I don’t think there’s a backdoor now.
Tor allows anonymous P2P, email, IM, and IRC chat. Given the U.S. Navy origin of Tor, there was suspicion of a backdoor. The source code is open so I suppose suspicion can be set aside. One guy in Paris was using a Tor router as an outside gateway doing requests for anonymous Tor users. The police searched his house and took him to the police station for a day. In the mean time, they searched his hard drives and other storage devices. The police then asked him if it was possible to trace back the criminal who downloaded the video. The Tor network is designed to keep no log of traffic. He was released the next day.
The level of secrecy is rather tight, but I wouldn’t consider it watertight.