Just rode down to my local bike shop to replace the 6 speed cassette that I didn't replace when the chain broke. Apparently they have a similar lifespan. My newer chain was skipping over my old cassette. It's the cleanest part on my bike!
@wkoetsch All you need to do is get a chain checker if you want to do it yourself. Your LBS should check your chain for free too if they are nice. That will tell you exactly when to change it. Checking every 500 miles or so isn't a bad idea, but remember to keep your chain clean and well oiled. That will keep it from stretching quickly
@wkoetsch Yes! Cassettes and chains have similar live spans. Chains start to stretch and the spacing starts to get wider and wider. Now, this effects the cassette that is designed for a normally spaced chain. Your cassette will start to wear and the teeth will become less defined, this is when a chain will start to "skip" on the cassette.
I'm not sure how it is on older bikes, but for modern ones you want to replace the chain at about 2k - 2.5k miles. Have it checked by your local bike shop ever 1k. Cassettes should last about 2 - 3 chains.