Apart from feeding it some oil now and then (probably to stop the irritating squeek) I reckon the chain has to be one of the components given the least amount of thought. Unless it gets really really worn or you're particularly unfortunate it'll keep turning your wheels until you decide to get another bike...but if you're like me and have a bike that you love and would rather not spend pots of cash maintaining it then please read on!
The last few days have seen a couple of bikes arrive for repair with the same fault caused by the same easily remedied problem, they each had chains which were so very worn that they had started to wear away the rest of the drive chain ( the chainwheel and rear derailleur/ jockey wheels). Its easily preventable and if caught in time will only cost you the price of a new chain (£20) rather than the cost of a derailleur/ jockey wheels and chainrings (£50+....+ fitting)
Worn jockey wheels have pointed teeth (left) rather than nice square edged teeth like the one on the right.
A little further investigation will probably reveal a worn chainset, on this one you can see that the outer rings are far more worn than the inner probably as a result of far more use of those gears.
Eventually a combination of a worn chainset, a worn out chain and damaged jockey wheels will result in missing gears and a slipping chain...which can prove a little painful. The answer is very simple, periodically check the chain for wear- it doesn't require any special tools and only takes a minute or two. To check your chain all you are going to need is a chain and a 12" ruler...here's how...
Prop your bike so that it'll stand on its own, then rest your ruler along a length of chain. If your chain is in optimum condition it should measure 12" for 12 complete links- when measured from/ to the centre of the link. Unless new most chains when measured have stretched a little- if its anything more than 1/16th inch then you need to think about getting a new chain.
....Just in case you're not sure- this is one complete link, count twelve of those and then measure.
I'm not sure what the average life of a chain is, as with most things it depends on the quality of the chain, how well its been looked after and the punishment it's endured. I do check and oil mine but commute daily in all weathers- so tend to check it monthly and change it annually.