Linux/Free games

Free games from repositories
To download and install programs on Linux, one typically does not download executable files from various websites and run them by hand; instead, distros provide a software repository or package manager. If something is not in your distro's manager, you can still port the package over but you might need to puzzle out some missing dependencies. For those of us who love to tinker on the engine more than driving the car, you can get the source code for each of these and compile it by hand.

Free games in distro-agnostic packages
These are still typically free software (or at least freeware), but do not use your easy-peasy package manager to install itself deep in your system. Most of the time, they are just binaries (or executables in Windows parlance) in downloadable tar.gz archives (which work like .zip files). Though, in some more rare cases, these may also include games that come as source code only -- you need to hunt down the right libraries through your distro's package manager, compile, and install manually (while trickier, this has the added bonus of increased optimization for your computer hardware, however marginal).