Does the Ripple protocol allow listing an account's (address's) past transactions? If yes, is there a web site for this? There are many well known sites that show balance and past transactions for a Bitcoin address, eg. blockchain.info, blockr.io etc. Does something like this exist for Ripple? Is this even possible with the Ripple protocol?

I know about http://rippledb.com/, but this doesn't seem to list this, just ledgers.
Yes, the Ripple protocol does allow you to list all past transactions performed. The most typical way would be to use the account_tx command. You can "page through" the data, retrieving a particular number of transactions per command, until you get to the first transaction.

I am not aware of a website where you can trace through an account's transaction history using GUI-style navigation, although the Ripple Charts Account Explorer will show you an account's transaction stream.