On a bike there are three kinds sprockets that the chain comes into contact with: the chainrings, cassette, and derailleur jockey wheels.
It seems that the standard practice is to replace the cassette for every 2-3 chains or so. Chainring replacement is heard of less commonly, and it seems they last much longer than cassettes. Why is this so?
In fact, it seems counterintuitive since each (given a 2x10 setup) each chainring is used on average five times more than each rear cog.
I can perhaps think of a few possible reasons:
Rear cogs experience more wear since they are smaller, so there is much more force on each tooth. (However, this doesn't apply to mountain bikes, where several of the rear cogs are bigger than the smaller front chainring) (Edit: in fact, this really isn't the case for XC mountain biking with a lot of climbing, in which much if not most of the time is spent with a front:real gear ratio of less than 1:1.)
There is more wear and tear from the chain pulling on the teeth (rear) vs the teeth pulling on the chain (front)
Front chainrings are made out of more durable material.
Finally, there are also the derailleur jockey wheels, which no one ever seems to replace, except when replacing the whole rear derailleur. I assume that's because they aren't a "load bearing" part of the drivetrain like the cassette and chainrings are.