From my experience I would say the order of wear goes chain, cassette and chain rings. On my road bike I go through about three chains before I replace the cassette. The chain rings last a long time on a road bike, especially the large one.
On my mountain bike the same is true for the chain and cassette, but I spend about 80% of my time in the middle chainring. I have to replace this about once a year. The grunge and sand really shortens the life span of a mountain bike drive train.
I have found it is cheaper and more realiable to periodically change your chain, than to let the cassette wear out. Cassettes cost $$$. Buy a chain ruler, it is money well invested.