The blockchain.info API allows for querying information about a particular Transaction by its ID. But if you want to follow the coins to the next transaction, I'm not seeing what the next query should be.
Each "out" of the transaction has an address associated with it, and you can query for details about a address' recent transactions. But if you're exploring deep in the past, the most recent 50 transactions for a given address won't have the spend for that particular "out".
So is there another API out there that allows you to query Transaction details based on "has transaction N as an 'in'"? Or do I need to go through the blockchain and make my own cache?
Edit: Blockchain.info clearly has the link to the transaction that spends a given output in their database, since the HTML view of a transaction now has "spent" tags after outputs that have been spent, which are links to the next transaction. However, that particular bit of data is not in the API view of the same transaction.