Bitcoin faucet
Used to gives bitcoins out for free to each visitor. IP addresses that receive bitcoins were recorded, so that bitcoins were given only once to each address. It was operated by Gavin Andresen, however it is not functioning as of Jan 30 2013.
For Testnet there exists a different faucet that is working which gives out coins for people who want to do tests on the Testnet. The testnet faucet also has a simple wallet available to hold testnet coins.