As Art mentioned, old computers do make good network attached storage devices, but they can also be used as print servers, game servers, or media servers. If your computer runs silent enough you can just hook it up to a stereo system and play music through it. In my opinion, using Windows 98, ME, or 2000 probably works the best, because they don't require too many resources, you can easily install VNC on it, or you can use
BrowseAmp or similar software on it to control it over the LAN. Plus, you really don't need anything more than a P2 for this.
If you watch lots of video podcasts, or have a lot of recorded TV, or record TV yourself, you can use something like a P3 or better, and Windows or Linux will work equally fine for playing videos into your TV. I hooked my neighbor's old Athlon computer into my TV using a spare graphics card and it played all my videos fine in both Win 2k and Linux. I've since replaced it with a P4 and am putting my TV tuner card into it for
mythTV purposes, which is very slick.
Learning Linux is also a fun thing to do, but if you're looking for
useful things to do with your computers, modding them into various different devices like mp3 players, file servers, other servers, etc is very useful. I'm planning on taking an older computer and putting it into a smaller case complete with speakers that can be a portable mp3 jukebox for robotics meetings that everyone can queue music onto.