In the column about why internal organs are not symmetric within the body, Cecil mentions that 99% of animal species are externally symmetric. Which ones are not?
My first thought would be animals with spiral shells.
Snails and slugs have their breathing holes on one side only.
And there’s a Wiki article here.
Sponges are notable, lacking symmetry because they are sessile.
The other examples in the article all seem to be minor asymmetric features on animals that are broadly symmetric.
Animals with radial symmetry - starfish, urchins, sea jellies…
I think those radially symmetric animals are also bilaterally symmetric.
ETA: although I guess that’s only technically true, since there is no unique plane of bilateral symmetry, and the development of radially symmteric animals is quite different.
Not sure if this counts under the definition used.
Flounder. They start out with eyes on either side of their head, but as they mature one eye migrates to the other side so they can still see while lying flat on the ocean floor. The other side of their body changes because they are lying on it, although I don’t know if there’s any change other than pigmentation on that side.
Just how do you divide an animal with five-fold radial symmetry into something bilateral? (Thinking of the starfish)
Since the arms are straight, a starfish has five planes of bilateral symmetry, running down the midpoint of each arm and extending through the midpoint of the gap between two arms on the other side. (If the arms were curved like a five-pointed “swastika” this would not be true, of course.)
I’m only making a statement about superficial geometric symmetry. I realize that from the standpoint of evolution and development the radially symmetric animals are quite different from Bilateria.
ETA: I’m rusty on evo-devo. Starfish are in fact Bilateria. This appears to be a secondary return to radial symmetry. The larvae are not radially symmetric.
Band saw?
Ok, here’s an evoloutionary overview.
http://tolweb.org/Animals/2374
We have Porifera (sponges) and Placozoa without any symmetry.
Then Cnidaria (jellyfish etc.) and Ctenophora (comb jellies) with radial symmetry.
Other animals fall under Bilateria, descended from a common ancestor that evolved bilateral symmetry. Within Bilateria there are some interesting cases like the adult starfish that returned to a radially symmetric body plan, and molluscs with spiral shells. As well as countless examples of more minor deviations from bilateral symmetry.
(On the one hand, the OP didn’t say we couldn’t consider fictional species; on the other hand, the question wasn’t posed in Cafe Society; but on the gripping hand, Moties were the first such species to come to mind for me and are the classic example [in science fiction, anyway] of a species that does not have external bilateral symmetry.) 
The Moties would presumably fall among the alien equivalent of Bilateria. A basically bilaterally symmetric body plan, with asymmetric features that are reminiscent of the fiddler crab’s large claw and the flounder’s eye arrangement.
IIRC (because it’s been a long time since I read the books), the Moties, (including the various subspecies) were genetically engineered.
There’s an open access review here on the genetic vs environmental basis for the development of asymmetric features among Bilateria. I haven’t had a chance to read it yet, posting in case anyone is interested.
https://royalsocietypublishing.org/doi/10.1098/rstb.2015.0417
Or, C5v has 5σv, whereas C5 has none.
Has no one mentioned humans?
My left acorn hangs lower than my right one.
(And causes me to trip all the time…) 
How about owls? Even though they have two ears, one is higher and farther back on their head – helps with stereo location when they hunt.
That seems pretty unique, and I think kind of a grey area. Most of the owl is symmetric, and ears are kind of like accessories.