lph is generally right, but I will generally go through 2 -3 chains before I need a cassette change - with a SUPER thorough cleaning of the cassette and checking for wear when changing the chain.

I've gone through about 4 cassettes and 8 chains on one bike (replacing chain at 2500 or so miles, when stretched) before needing to replace rings. Even then, you may not need to replace all the rings, just the ones that are most worn.