You probably won’t need your driver’s licence when backpacking but if you do intend to drive your regular licence and passport should be fine. I have driven in the USA with my British driver’s licence and vice versa without any problems.
Some countries, however, may require and international driving permit. This is pretty much just a translation of your regular licence into various languages. It also has your photo inside, which could serve as an id in an emergency, plus it lists all the classes of vehicle you are allowed to drive, useful if you want to rent something like a motorcycle (or a bus, perhaps).
Check with your local automobile club, for example, 
The AAA in the USA or 
The AA in the UK for more details.
