-rtorrent. Not only is rtorrent one of the most powerful bittorrent clients I've ever used, but it's also command-line based and easy to configure and walk away from. Run once and walk away, basically. Keep seeding those Debian CD's, boys! More bandwidth on the ports!
-Internet radio. You could run your own with Icecast if you feel like playing a random jukebox across your stereo systems, or you could listen to one already on the net. My favorite is SomaFM (Groove Salad!) and there's a variety of codecs to choose from. I use the AACPlus 64k stream just because my bandwidth is in low supply, but I imagine an MP3 stream would be easier for some older computers.
To play Groove Salad, I install MPlayer, and then I get the download location of the playlist SomaFM gives me and I give that to mplayer.
And it's off. Plug in some stereos and you've got an internet radio player. Alternatively, you could use the MPlayer options to record the music stream for later listening, like this:
mplayer -playlist http://somafm.com/groovesalad32.pls -ao pcm:file=mystream.wav -vc dummy -vo null
Keep in mind this fills up pretty quickly, though, so make sure you have enough hard drive space to leave it running! After you're done recording, you could break it up with Audacity and encode it with Vorbis tools or LAME for a portable music player.
-Newsbeuter has some downloading options I haven't played with yet, but if you have podcasts or a netlabel you follow in your RSS feeds, you could set Newsbeuter up to download them for you so they're ready to be listened to.
-Games. Actually, it's funny how handy it is to have a server lying around for games, especially if my friends come over and want to play Minecraft together. Most games have Linux server options.
But there was another option I had in mind. Console games like Dungeon Crawl Stone Soup tend not to use much (if any) computational power, but there are some like Dwarf Fortress that are pretty heavy on the processor. DF isn't purely text out of the box, but you can mod it to be so. Dwarf Fortress is a very powerful simulation game that requires more power than your usual used computer can handle, so this is a great idea for situations where your laptop is less powerful than your desktop.
Any other ideas?