Applications developed on Ethereum
There are various implementations of DAOs and smart contracts in Ethereum, most notably, the DAO, which was recently hacked and required a hard fork in order for funds to be recovered. The DAO was created to serve as a decentralized platform to collect and distribute investments.
Augur is another DAPP that has been implemented on Ethereum, which is a decentralized prediction market. Various other decentralized applications are listed on http://dapps.ethercasts.com/.