Recommended Version for Mac OS X 10.5.8 I am wanting to download and learn how to use Blender at home on my Macintosh PowerPC system.  It is older so I need to know what version of Blender is recommended for my system, here are the specs:

Macintosh
Dual 2.3 GHz Power PC G5
OS X 10.5.8
2 Gb DDR2 SDRAM

Video Card:
NVIDIA GeForce 6600
VRAM - 256MB
32 Bit Color Depth
General hardware age isn't the big problem here, and that's what the other commenters were talking about. Their advice is great if you have an x86 system of that vintage (ex, Pentium 4), but you don't. You have a PowerPC machine. That's problematic as the official OS X Blender builds are not compiled for PPC and haven't been for quite some time. Since 2.63, to be exact. You can find it here: http://download.blender.org/release/Blender2.63/

Download the file blender-2.63a-release-OSX_10.5_ppc.zip and install as usual. It should be your best bet.