It doesn't have to be an Intel based Mac to run OS X. OS X has been around for about 6 years, so the PowerPC Macs can run them just fine (since that's what was in the Macs before the beginning of this year, which is when the Intels were introduced).
As for what the cutoff for the Macs are, check the system requirements for Mac OS X on Apple's website. Each version (10.0, 10.1, 10.2, 10.3, 10.4) has certain system requirements. As far as upgrading, every 10.x version is a major upgrade so it requires purchasing (For example, to upgrade from 10.3 to 10.4, you have to purchase 10.4). Every 10.x.y version is an upgrade for that particular "10.x" version (in other words, if you have 10.4.x, you can upgrade to the latest 10.4.7 version for free. If you have 10.3.x, you can upgrade to the latest 10.3.9 version).
Any G4 Macintosh will be able to meet the requirements to run Tiger. Just be sure to upgrade the RAM to as much as possible, especially if it's one of the first generation of G4 Macs.