Is there a remote Bitcoin API that doesn't require anything to be stored locally? What I imagine is a trusted centralized server (say run by Mt. Gox or some other exchange), that exposes a simple medium/low level API (let's say in JSON):


getTransaction(fromAddress)
getTxDetails()
executeTransaction()
...


I know BitcoinJ does't store the whole blockchain, but it does store and update the headers. The method I seek will save me the hassle of managing any local data except the actual keys/addresses.

I would not have to give this transaction my private key, but rather use some sort of Offline Transaction equivalent. Is there something close to this? Is somebody building this? (If not, someone should!)
This question is a little old now. But you could use the blockchain.info JSON RPC api. It is designed to be compatible with the original Bitcoind implementation and most functions can operate without private keys.

http://blockchain.info/json_rpc_api