This is a very incomplete list. To install 40x more games, open Linux Mint PPC's Software Center and install everything you could like.
Beware with games like OpenArena, they will be very SLOW if you don't have any 3D support, altough it can run with an 16mb video card with the effects set down to the lowest settings possible.
To install these games, connect your Linux based PowerMAC to a internet connection, open a terminal and type the specified command.
Battle for Wesnoth.
An turn based strategy game, similar to Heroes of Might and Magic.
Command: su -c 'apt-get install wesnoth'
PrBoom
A Doom engine.
Command: su -c 'apt-get install prboom'
You need a working Doom WAD file. You could play the original DOOM I/II coying the WAD file to /usr/share/games/doom. Open the file manager as root with the command "su -c 'pcmanfm' " , and then copy the files.
Here you have a FREE as in freedoom (NON commercial/pirated/whatever) WAD file, which will allow you to play DOOM personal IWADS (MODS).
http://www.nongnu.org/freedoom/download.html#
Download the complete IWAD, unzip the file, and copy the WAD file to /usr/share/games/doom
I have to say that the free implementation of the Doom game "media" is pretty cool, and some levels are impressive for a 20 yeard old game engine.
Widelands
Tactic building / fighting strategy game. Build and develop a village and expand your little empire.
Command: su -c 'apt-get install widelands'
BosWars
Another RTS game. Think like an StarCraft like game made with the Warcraft II engine. Not bad.
Command: su -c 'apt-get install boswars'
Scummvm
Adventure game engine. You know, with that, you could play LucasArts adventures like SamNmax, maniac Mansions, Sierra games, Gabriel Knight, Myst...
Documentation: http://www.scummvm.org/documentation/#
Command: su -c 'apt-get install scummvm'
Residual
Like Scummvm, but just to play Grin Fandango
Command: su -c 'apt-get install residual*'
Supertux
A Super Mario Bros clone, but with the Tux penguin. Tons of levels downloadable for free, ingame :)
Command: su -c 'apt-get install supertux'
OOLite
Needs OpenGL but a G4 could handle it on software. It's an Elite
clone. You are a space pirate and you have to conquer the galaxy.
CorsixTH
A Theme Hospital engine. You need to copy the original folders from the CD, and paste them to the desktop. Then, open CorsixTH to specify where you copied the folders of the CD-ROM.
Command: su -c 'apt-get install corsix-th'
OpenTTD
Transport Tycoon Deluxe reimplemented with ZILLIONS of maps, transport and such downloadable from within the game. A MUST have for a simulation games lover.
Command: su -c 'apt-get install openttd'
FreeDink
Dink Swallod. A top view RPG with some gameplay which looks like Zelda. Pretty good, and there are tons of free mods for it.
Command: su -c 'apt-get install freedink'
Nethack
Well, the classical roguelike. Two much to explain here. Play it,
die a lot of times, and play it again too die in a more ridiculous
ways. Not sure if it's a game or an accurate fatality simulation project about how many different ways could a player die.
Command: su -c 'apt-get install nethack'
Dungeon Crawl
A roguelike like Nethack, but more focused on combat instead of exploring-
Command: su -c 'apt-get install crawl'
FreeCIV
Civilization clone. Build your empire since the beggining of the times
until either you reach Alpha Centauri or conquer the world.
Command: su -c 'apt-get install freeciv-client-gtkfreeciv-sound-standard freeciv-client-extras'
Assault Cube
A Counter Strike clone, very playable under a PowerMac w/ Linux Mint AND a very LITTLE 3D acceleration.
Command: su -c 'apt-get install assaultcube'
PangZero
A Pang clone. Break balls into two smaller ones with a hook until you
remove all of them.
Command: su -c 'apt-get install pangzero'
Abuse
You know Metroid? Well, you will find that kind of gameplay there.
Command: su -c 'apt-get innstall abuse-frabs abuse-sfx'
PySol
Huge solitaire card game pack.
Command: su -c 'apt-get install pysolfc'
Ltris
Tetris. That's it. Even your mom played it.
Command: su -c 'apt-get install ltris'
Frozen Bubble
Puzzle Bubble clone
Command: su -c 'apt-get install frozen-bubble'
Eboard
A chess game
Command: su -c apt-get install eboard eboard-extras gnuchess fairymax'
More games will come soon.