Can you unlock an Apple iPhone and use it with another wireless carrier?

Yes, you can do it free.

The original 2G iphone is easiest to unlock. Software such as QuickPWN can unlock an iphone to be used on any GSM network.

However, the 3G iphone requires a software unlock. The baseband is updated with every iphone update, so it takes longer to find a solution. However, it is currently possible.
You can unlock an iphone by calling your carrier and asking them to submit a unlocking request. It can take up to seven days for the request to go through.