I change the chain when it starts to perform badly, which typically happens anywhere between 1800 and 2600 miles. I change the cassette when changing the chain doesn't improve the bad performance, which usually works out to around 2 or 3 chains, or 3600 - 6200 miles. I have never changed the chainrings on any of my bikes yet, and I've got over 20,000 miles on most of them.
Edit: an associate of mine who's a kickass mechanic recently suggested that I just change chains every 2 or 3 months, and buy cheap KMC chains. Since they're expendables, he figure's treat 'em as such.