When you add numbers together you start at the little end. Imagine a bignum implementation with multi-word numbers. Now imagine you have a bunch of them in a file you want to add up. If the numbers are in little endian order you can do a streaming implementation that reads and adds at the same time. If they are in big endian order you need to read a whole number before it can be added to the accumulator.

Obviously this example is very contrived. This sort of thing was much more of a concern on 8-bit computers. But little endian still seems more natural to me.