How do I determine the balance of an address I don't own? (WebAPI or local API)
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