1) It's cheaper; ie, pennies to send a transaction of any size, not a fixed 2-3%. As someone noted above, merchants could pass those savings along.

2) Consumers do not expose ANY sensitive information when they execute a transaction, unlike every means of electronically sending fiat. As a consumer, I will not use a credit-card on sites that I don't have a good reason to already trust because I know that I'm handing them everything needed to steal a bunch of money from me if they're dishonest (or simply lax in their own IT security). Yes, there's recourse with credit-cards if fraud happens, but even in the best case scenario, it's a big pain to correct; and in the worst case, far more than my transaction amount can be lost.

3) Privacy (pseudo-anonymity), potentially.