Fiddler crabs aren't profoundly asymmetrical as compared to other species, it's just that one claw is significantly larger than the other - like you mentioned it's largely redundant except for mating displays, and probably arose through chance mutation/adaption a few million years ago, but yes almost every organism is inherently symmetrical.
Imagine cell multiplication as two sets of numbers: -
1 2 4 8 16 32 64 128 258 512 1024, etc
1 2 4 8 16 32 64 128 258 512 1024, etc
Given enough generations, the numbers will be arbitrarily high (in terms of cell numbers) that if one set of numbers skips a doubling, the resulting numbers will be marginally different, so the two sets will be roughly the same amount (e.g. size), so making the organism symmetrical - from what I remember from A level biology anyway
However, nature always finds a way to contradict a set pattern, so if you want whacky creatures, check out the
Burgess shales :eek!!!!: