No problem. I use to do it all the time between Washington state and British Columbia (both directions US/CDN hired cars). There are always restrictions about taking a US car into Mexico of course.

However, if you're intending on driving it across NA or across country (USA), you might want to write a quick email to AVIS to double check. I don't think they have issues with it, but I do remember renting cars from Thrifty-IAH and reading that they needed to know if you're going to take the car outside of Texas or Louisana states (or there will be penalities).