There's also a method of counting where you touch your thumb to the sections of your fingers on the same hand, which naturally lends itself to base 12. This can be extended by keeping track of how many times you've counted to 12 on the other hand, which lends itself to either base 60 or base 144.

Interestingly, the Sumerians did not seem to employ this method, they would count 6 instances of counting to 10.