FBinNY 

There's lots of legitimate debate on this subject, and a number of approaches to getting the most piles for the total chain and sprocket dollar.

1- the most common approach - is replace chains when they wear to a measured 1/2% stretch (1/16" over 12") and replace them. Replacing at 1/2% stretch usually does a decent job of saving the cassette, and most are able to use the same cassette for 3-4 chains.

2- run forever and replace all. Run the chain and sprockets until they give up the ghost and start skipping. Usually this is well past the 1% stretch point, and can be as much as 2-3% stretch. the method can be surprisingly economical, but if carrier too far can also mean replacing the chainrings (or at least one) too.

3- the 2 (or more) chain theory. This combines elements of the other 2 approaches and is the most economical method, especially if you have reusable connectors. use 2-4 chains and rotate them at intervals well short of where they'd reach 1/2% stretch. I rotate 4 chains every 1,000 miles on my commuter. This is a big expense at the front end, but generally allows you to run all the drivetrain components until the chains all reach 1.5-2% stretch. It also has the benefit that chains can be properly washed, dried and oiled at your convenience while out of the rotation.

The worst method is to run a chain to about 1% stretch, and then replace it. By now the cassette is beyond saving, so you might as well leave them together and adopt the 2nd approach.

Which method makes sense for you depends on how much you ride, how long you keep your bikes, and the relative cost of chains, cassettes and chainrings. years ago, the use until it dies made sense since freewheels were fairly cheap, but with today's expensive cassettes methods 1&3 make more sense.