There's binary, decimal, hexadecimal, anything else?
Octal (base-8) is another popular one, but there are infinitely many numeric systems.
For example, in Excel the columns are labeled in hexavigesimal (base-26).
Here is a list of popular positional numeric systems.
Then you also have other numeric systems that aren't positional, such as Chinese and Roman numeral systems, but I'm guessing by your examples that you meant strictly positional numeric systems.
You can use any base you like to represent numbers, though it becomes difficult once you move beyond the alphanumeric characters. On the other hand, if you consider a single byte as a "digit", then most (unsigned) integral numbers are stored in base-256 within a computer.
That being said, the only widely-used number system aside from those listed (that I'm aware of) is Octal, which is base-8.
The Babylonians liked base 60 (sexagesimal)...
http://en.wikipedia.org/wiki/Babylonian_numerals
There are infinitely many...check out the Wikipedia page for Arity (specifically n-ary):
Arity - Wikipedia
There are tons of bases for integers (with pretty much everyone knowing base 10).
Also complex, real, & rational.
Wikipedia Number
A numbering system can be formed for any Number n, where n need only be an element of the Hamiltonians or any subset thereof the digits then correspond to the form
{n^k0, n^k0-1, n^k0 -2, ... n^0}.(radix point){n^-1, n^-2, ...,n^k1}
Where k0 is the High order of magnitude, and k1 is the precision
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