Are you asking why we use a base 10 system? or are you asking why Arabic numerals are favored?

If the latter, languages that don't use a Latin alphabet normally do have their own set of numbers. 一，二，三，四，五 is 1, 2, 3, 4, 5 in Chinese and Japanese for example. When you do see Arabic numerals (side note, Arabic has a different set of numbers too I think) in, say, an Asian country, it is often in areas with a high volume of foreigners (like Airports). The permeation of Western culture has assured that western numbers are pretty broadly recognizable.

I believe Arabic numerals were brought to Europe by way of Italy and their interaction with Northern Africa.