The first bitcoin transaction ever was in block #0. It was the “coinbase” of the block, the payout transaction that gives newly created bitcoins to the miner that mined the block.

However, that’s not very interesting, since most blocks have a coinbase transaction. I’m guessing what you’re really asking is what the first non-coinbase transaction was.

The answer to that is this transaction in block #170. On January 12th, 2009, this transaction transferred 10 btc to Hal Finney from the creator of Bitcoin, Satoshi Nakamoto.