Why do we count in 10's? Obviously because we have 10 fingers. It is not though preordained that we should count in 10's.
The Yoruba people of West Africa have a number system based on counting in 20's.
Computers use binary code, counting in 2's - using the symbols 0 and 1.
<> Clocks use 60's and 24's - 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day.Angles use 60's and 360's - 60 arc seconds in an arc minute, 60 arc minutes in a degree, 360 degrees in a full turn.
Currencies mostly use the 100's - 100 pence to a pound etc.
Natural systems use lots of different bases. DNA can be written using 2's or 4's, there being 22-4 different bases which make up our genes.
There are subatomic particles called quarks, of which there are twelve, so could express quarks in base 12.
Hexadecimal or base 16 - using the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F is also commonly used in computer programming.
The Fahrenheit Scale Goes from 0 to 212, and there is a very special number, e=2.71828...., called the natural base, which occurs in many areas of maths, physics, biology and chemistry.