Any Mac that can run Panther can run Tiger, that's the thing. Even a Power Macintosh 7500 with a G3 card can run Tiger.
Tiger may be the most compatible OS Apple has ever released. 1995-1997 (with a CPU upgrade) and 1997-2007 (stock CPU).
It's sort of a special version of OS X. It still runs Classic Environment, it runs on so many different Macs, it still has AppleTalk printers.
Leopard is also quite compatible too. I've never heard of it running on a beige Mac but it can run on a Blue G3 with a G4 upgrade and a video card upgrade. So that gives you 1999 (with CPU upgrade) and 2000-2009 with non upgradable G3 Macs excluded. You don't even have to use any hacks at all except for one Open Firmware change if your CPU is less than 867 MHz.
Compare these to Snow Leopard, which runs on 2006 and up. That's why it's such a a harsh cutoff in comparison.