I'm looking to make a faucet website, but was wondering what is the maximum number of output addresses one can send to with one bitcoin transaction?
Today the modern Bitcoin-qt client does not relay transactions with more than 200 outputs. But this is not protocol restriction. You can create transactions up to 100k size, which gives you 2500-3000 outputs (try to count the exact number yourself).
For example, tx https://blockchain.info/tx/0313e6552a5337de92c475c0dbbb0e351a1525b0f202beb9d4c75b3a5b114bf3 has 2501 outputs and was successfuly mined 3 days ago
You add to size of the transaction as you add more addresses, and eventually increase transaction fee.
If you don't add a minimum transaction fee, and your coins do not have enough confirmations then your transactions would be delayed for a day or more.