Cassettes.  If you are replacing your chain after it has become worn out, the chances are you will need to replace your cassette also, and in any case it is good practice to do so. 

Chains and cassettes wear together, so often, when you fit a new chain to an old cassette, you will find the new chain 'slips' under load.

You might not need to change the cassette if your chain has broken when still quite new or is being changed with only a few miles under its belt, but it does no harm to change the two together anyway.

Mountain bike, tourer, hybrid cassettes

Road cassettes