Adanaxis is an open source space shooter game that lets you move in all 4 axis, or rotate continuously along any combination of axis. All models are 4 dimensional.

Needless to say, it is confusing to the point of unplayability past a certain point, but utterly fascinating.

You can grab a copy from your Ubuntu, Fedora, or Arch repos, and it is certainly worth trying to wrap your head around for an hour or two, if you are into that sort of thing.