How do I determine the balance of an address I don't own? (WebAPI or local API) I have an arbitrary address.  How can I get the current balance of the account through a Web API? ... how do I get it for a local API?

I'm also interested in all transaction history for that address.  Let me know if the API can offer that as well.
You can query the unspent outputs of an address with this:

 http://blockchain.info/unspent?active=$bitcoin_address


You can get the transaction history for an address with this:

 http://blockchain.info/address/$bitcoin_address?format=json


For more information see http://blockchain.info/api/blockchain_api