Bitcoin's blockchain is basicly just a mechanism to record timestamped entries. Bitcoin uses it as a transaction ledger, but it could be used for many other things.
For example, one could create a chain for a decentral chess-game, where each move is an entry in the blockchain. All nodes can verify if the players turns are by the book, and in the correct order, and decide who is the winner.
Can anyone think of other examples of alternative chains?