Building Distributable Linux Binaries?

Grubby Games asks: "I make games for a living, and I want to ensure that my games will run on as many Linux distros as possible. However, since I distribute binary game executables, the programs often fail to run on certain distros because of missing dependencies, and so forth. So, how do the Slashdot Linux gurus handle this situation? I've heard a number of theories on the subject, but have yet to find one that results in 100% cross-distro compatibility. Is it even possible, short of distributing source code?"