Given a Bitcoin address or a record of a transaction between two Bitcoin addresses and a website like blockr.io to explore it, is it possible to identify what online wallet service a Bitcoin address belongs to? For example, is it possible to say that a transaction was send from a Blockchain.info Bitcoin wallet to a Coinbase Bitcoin wallet?
No, generally this is not possible. Every Bitcoin address is randomly generated and carries nothing identifying the party that created it.
In principle it might be possible to infer something based on other addresses that sent coins to or from the address in question, if you know something about them through other means.