It all depends on where you're going. There are a lot of different auto clubs in Europe that have a relationship with AAA, each with varying level of benefits. One option could be to get coverage from the AA (United Kingdom), that offers both UK coverage and European coverage on a short term basis. You can find info here.
To find a list of other auto clubs in Europe that are affiliated with AAA, please click here.
You also can inquire with auto insurance agent about liability and roadside coverage. I know that many US automobile policies cover you as a driver in a rental car, but typically just in the United States.
Finally, you can inquire with rental car companies as to liabiity and roadside coverage costs.
Have a great time!
Stephen
P.S. Sorry, it took so long to respond. Had to do a lot of digging on this!