Some international carriers are beginning to offer free downloads for smartphones that will detect when an international call is being made and automatically route the call to a 'dial-around' access number for completion over their network. This works the same as using a calling card except the software in the phone does all the access number and PIN dialing rather than the user.

One such carrier is Tel3 Mobile. For international calls originating from the US it's hard to beat their rates. They route calls over the traditional voice network instead of the internet and so the sound quality is the same as a regular cell phone call. You can try their service for as little as $10.

Another is PhoneGnome. Their main business is home and small business VoIP service but they've developed a download for smartphones that automatically routes international calls to a US access number for completion over the same network as their VoIP customers. They also have a product called "Mobile Web" that will work with any cell phone that has internet access. For payment you can choose between pay-as-you-go starting as low as $5 or one of their flat monthly fee plans.

I've been collecting other information on smartphone international calling plans here:

Cell Phone International Calling Guide - Smartphones