Heavily based on Quake III Arena, Open Arena is, well, Quake III Arena. That about covers it. Okay, there are slight differences. The game characters and maps are different, but the concept and game play are pretty much identical.
On my aluminum Powerbook (1.5 GHz, Tiger), this performs really well in a 640 x 480 resolution. In tweaking the settings (not just in Open Arena but in everything reviewed here), I found that screen resolution and the number of opponents are by far the biggest factors in getting good frame rates. So adjust accordingly. The game is a 460 MB download, and there's also a single player mod called OARemix available at Mod DB. OARemix is a separate game folder where you copy the OpenArena.app into it and play with all new maps (the one on the oil rig is really good).
If you're having trouble getting sound, turn OpenAL off in the Sound settings, and if your mod doesn't have that setting (like True Combat mentioned below), switch to the console with Shift + ESC and enter
/s_useopenal 0, then restart the sound with
Also, reader Peter S. compiled OpenArena for G3s (altivec disabled) available at this link.
(ADDENDUM: There's a Quake III mod that also works on Open Arena called True Combat. The physics and weapons are all about realism, and it's the best Quake III/Open Arena mod I've seen. Just download it and put the "truecombat" folder in your Open Arena folder, then start Open Arena and click "Mods." To do single player, choose "StartServer" under the Combat tab, and then you can choose your mission type and skill level. Further instructions are found on the True Combat features page.)
Cube 2: Sauerbraten is another title that's been in development forever and shows no signs of going away. It's much like Open Arena, though a major difference is the addition of a Campaign mode where you can progress from level to level.
This is slightly more resource hungry than Open Arena, and there's a wider disparity in frame rates from map to map. Most rendered well, but a few were very slow (You'll notice I resisted the temptation to type out a dozen w's at the end of slow. It always bugged me how much bandwidth that wasted.). When you download the DMG file, it installs as a simple app package. No need to hunt for binaries or change file permissions, so that's nice. Like Open Arena, the game play is very fast and challenging.
Nexuiz, or Nexuiz Classic, stopped development with version 2.5.2 when one of its developers left to develop a new version of Nexuiz with IllFonic, and those left behind created an new open source fork called Xonotic. But Nexuiz Classic is still available for download at Sourceforge.
Although Nexuiz comes with a nice in-game tutorial, I had real difficulty getting good frame rates out of this. I could really only play it with one bot, and even then it was iffy. So I didn't explore this one as much as the other two. Xonotic may be an alternative for Leopard users. I know they don't support Tiger, but Leopard PPC, I'm not sure (that linked post was from 2010).
There are other games out there, too. There's Aleph One, which is an open source update of Marathon. There's also Tremulous, which I haven't tried. Those alien spiders were a bit too creepy. Maybe later. Also, Alien Arena advertises OS X support, but OS X (and Linux) users must compile from source, and I found no references on the net of anyone succeeding. Maybe later.
The only one of these games I tried on Linux PPC was Open Arena. I got good frame rates, but the colors were all messed up. Apparently the Radeon driver doesn't agree with my ATI Mobility Radeon 9700. I'll be on pins and needles for bug fixes.