Yes you can, but only with AT&T at this time and some setup.

The primary set up step is to make sure that the email address associated with your Thwapr account is the same as the address that your carrier provides for your mobile device. When you signed up for Thwapr you may have put in your personal email so make sure to login to Thwapr from a computer rather than a mobile device and click on the "My Account" tab and change your email address to the correct one.

Here is the format for an AT&T MMS email address:

 your10digitmobilenumber@mms.att.net

ex. 5551231234@mms.att.net

Support for other carriers to use MMS may come in the future.