Wikipedia says Tiger was released in April 2005, which sounds about right. Before that was Panther, and before Panther a couple or few others.

I've been running OS X since 10.1 or 10.2 on my G4, and it will run Leopard, as well. Each new cat name runs faster on this machine than the cat name that preceded it. And each cat name has free updates before the next cash-money ($129 U.S.) release you could ignore for as long as you wish.

My G4 also runs OS 9 on another partition, and that old system was released in 1999. It hasn't been updated for years, but one browser, iCab, was recently updated for OS 9.

(My old G3 tower that I bought in the '90s, even before OS 9 had gone through all its updates, also runs OS X Tiger. I don't think it would run Leopard, though. It might, but I doubt Apple will support it officially.)

So you shouldn't have any concerns about being forced to lay out more cash for whatever follows Leopard. You'll be set for years. The system that follows Leopard will be evolutionary, not revolutionary, as X is to OS 9.