The minimum requirements for Apple's OS X Leopard are an 866Mhz G4 processor and 512MB of RAM. I happen to have an aging but still nice 1Ghz Powerbook with 768MB of RAM. Loading Leopard on it should tell us just how accurate those minimum specs are.
Tiger: 40 seconds to login screen and 9 seconds to shut down.
Leopard Install: 1 hour, 14 minutes, 23 seconds (about 2x what it was on my Macbook Pro, but short compared to the 3+ hours it initially reported).
Leopard: 50 seconds to login screen and 11 seconds to shut down.
Basic use: Using Cover Flow with Safari, iChat, and iTunes open and it's choppy. (Quick Look works well, though.)
That's not bad at all, but of course we have to wait for more exhaustive testing to draw any real conclusions. I'd say you're safe if you've got an older mac. RAM will help, but if you're counting the iLife and Leopard costs, you might just want to put that ~$200 towards a new Mac. Just saying.