Bicycles are wonderful, efficient machines but like any mechanical device with moving parts, those parts are subject to wear. In some cases, like when you pull on the brake levers and notice that it is taking longer to stop than it used to, you get a clear signal that something needs attention. Even the least mechanically empathetic rider tends to notice when they can't stop, so worn brake pads are things that call attention to themselves as they wear. The brake pads aren't the only part of the braking system that wears and elsewhere I've called attention to the problem of brake rim wear.
The bicycle chain is often ignored unless it's squeaking or refusing to shift into the proper gear but in the case of your bike chain, ignorance is not bliss. A worn chain may shift fine and not squeak but as the individual links wear, the chain becomes slightly longer. While this is commonly called "chain stretch" the additional length is not the result of any metal stretching, it's the consequence of accumulated wear of the bushings in each chain link.
Chain wear isn't measured in miles or months. Three thousand miles ridden over the course of sunny summer by a rider who spins in low gears and who cleans her drivetrain weekly is a very different situation than a thousand miles ground out by a commuter on the gritty, rain-soaked Seattle hills. The tool for measuring chain wear isn't an odometer or a calendar, it's the common ruler.
On a brand new chain there is 1/2 inch between each pin so twenty half-links should measure 10 inches (254 mm). If those 20 half-links sum up to 10 1/16 inches or more, it's time to replace your chain. While you can measure this with a ruler, a tool like the Park CC-2 Chain Checker makes checking even easier.
Modern derailleur drive trains have narrower chains and cogs (something I ranted about a few years ago), and the newer stuff really does wear faster than and cost more than the old stuff. So checking your chain is important.
If you let your chain go too long, what happens is that the old chain wears your rear cogs and maybe your front sprockets to match up with with its worn profile. Dirt on the chain works to wear the metal cogs. The pressure is most concentrated on the small cogs, so the smaller cogs and the ones you most use see the most wear. The insidious thing is that you don't notice it until your chain has worn to the point where finally your shifting gets sloppy or the chain breaks. And if you wait until then to replace your chain, you'll find the new chain won't mate with the old cogs (or at least all of your old cogs). The symptom you'll feel is a skipping or popping under load as the new chain tries to settle into peaks and valleys of the worn cogs.
Chains are cheaper than cassettes or chain rings and if you do your own maintenance, a chain checker is a good investment. And the mechanic down at your local bike shop who tells you that you should replace your chain even though your bike seems to be behaving fine probably isn't trying to rip you off. He's probably trying to save you money in the long run.
Keep 'em rolling,
Kent "Mountain Turtle" Peterson
Issaquah WA USA