It’s common knowledge that (most) modern societies use arabic numerals, and moreover use base 10 for counting. That is, you count from 1 to 9 (unless you’re a programmer and you start at 0) and then you use 10, which uses that 10's place.

I’ve learned about [base 12 counting systems](https://www.youtube.com/watch?v=U6xJfP7-HCc) recently, and even about [how Klingon isn't that alien](https://www.youtube.com/watch?v=l4bmZ1gRqCc) - because of its base 10 system! Making a counting system which is alien to humans infers *not using* one that has been used by humans. I can't guarantee an alien counting system unless I know what has been used.

In the interest of making alien math more believable and actually [alien](http://dictionary.reference.com/browse/alien?s=t), what counting systems have been used by humans, and why?