Worn Bike Cassette...

The cassette (i.e. your gears at the back) will eventually wear out, and one of the most common causes of chain slippage is a worn cassette/worn chain. You won't notice it immediately, but if your rear cassette has "Sharks Teeth", it's time for a new chain and cassette. The two pictures below show you the difference between a brand new cassette and a worn out one.

The brand new cassette has teeth which have a flat top which allow the chain to engage and not move. Over time, this flat top is worn away to a point which is when your chain will start to slip.

Once your cassette looks like this, it's a VERY good idea to replace both the chain and cassette. I can almost guarantee that if you don't change the chain at the same time, you're still going to get slippage. Change them both, that way you're starting fresh with both.

FAQ

Q. What causes this?
A. Cassettes won't last forever. They take a lot of abuse, but there are things you can do to minimise cassette wear. Clean your drive train often and keep it lubed up. Other than that, just accept that chains/cassettes are disposable and will need to be changed at some point.

Q. How long should a cassette last?
A. Depends. Some will last many thousands of miles, others will only last up to a thousand. It's all down to good maintenance. The better you treat your cassette, the better it will treat you.

Q. Is there anything else I can do?
A. Yes. If you're inclined, you can run two chains that get rotated on a monthly basis. Install a KMC Quick Link and mark a day on your calendar when you need to change the chain. This helps to spread wear across a number of chains, and also allows you to take the chain off and give it a good clean once a month. 

I've found that Chain Reaction tend to do the best deals on cassettes, particularly SRAM. Of course, all of the retailers listed below are excellent, so just go with the one who has what you want.