On a second thought. Is it safe to say that as long as I don't sell my game, I can use a remix of another song in my game and not worry about people trying to sue me? Assuming the game happens to become famous-
Any time you use something that you don't have a license to use (or don't own) you run the risk of legal action. How much risk? Well, that differs from IP to IP and company to company. Some companies are really strict while others are more lenient. Even if your game was completely free, simply distributing it is still a violation of copyright. The game doesn't even have to be "famous" to have companies send you a cease and desist letter.