most bilaterally symmetrical animals, while appearing superficially symmetrical on the exterior have a large degree of assymetry internally. you just have to look at a diagram of the human digestive system. even on the outside most species exhibit some deviation from symmetry. human males very often have one testicle that hangs slightly lower than the other for example (i had to check the stats on this to avoid potential embarrasment, only 27% of men have level testicles)

as far as superficial symmetry in animals goes, i would suggest the humble snail. their shells are based on a logarithmic spiral which can't be considered symmetrical and the pulmonata (land snails) have one pneumostome (respiratory pore), usually found on the right side of the animal.

Interestingly as far as I know no animal is perfectly symetrical. Even humans have one leg slightly longer than the other and for this reason if you are told to walk in a straight line blindfolded you walk in a circle. Most organisms have evolved perfect (or almost perfect) symetry because if they haven't movement will be difficult, particually with birds. The least symetrical animals are probably invertibrates at the bottom of the ocean that have not needed to evolve almost perfect symetry. Sponges are the least symetrical animal I can think of.

Most animals do look bilaterally symmetrical, with clear anterior-posterior and dorsal-ventral axes plus a third, symmetrical axis that is mirror-imaged around the midline. However few, if any, truly are symmetrical. First, most apparently symmetrical animals are found to deviate significantly from symmetry if measured carefully. Second, if we take our own bodies as an example, then while we approximate bilateral symmetry on the outside (reflecting symmetrical muscles and bones), our internal organs are asymmetric. This includes the heart, lungs, liver, stomach and the rest of the gut.

However some animals also show clear, organised external asymmetry. So which of these is the most asymmetric? One answer is the sponges, as most adult sponges have no organised axes at all. However this is somewhat misleading as sponges are thought to have diverged very early in animal evolution, before the three clear axes evolved: it’s not that they have evolved to upset bilateral symmetry, just that they never had it in the first place.

Amongst those animals that do derive from bilaterally symmetric ancestors, I suggest three frontrunners. Flatfish take the prize for the most asymmetric vertebrates as they are actually lying on one side. During embryogenesis an eye migrates from one side of the head to the other and the two sides develop startlingly different patterns. Also contenders are the snails. Snail shells either coil to the left or the right, and much of their anatomy is similarly asymmetric. However I think first prize should go to echinoderms such as sea urchins and starfish. Living echinoderms have a radially organised body, but fossils show these evolved from bilaterally symmetrical ancestors. During embryonic development their larvae are still bilaterally symmetrical. Then, at metamorphosis, the adult body pretty much dispenses with this organisation. Only vestiges of bilaterality remain, visible by careful inspection in some species.

 Fascinatingly, recent studies show that the genetic pathway that regulates the internal asymmetry of our own organs may also be controlling the extreme asymmetry of invertebrates like snails and sea urchins. It may be that most animals share a common mechanism for developing bilateral asymmetry, but that only a few display it prominently on the outside while most hide it internally.

I would nominate any one of the terrestrial slugs. The slugs, having lost their asymmetric shells during evolution, may appear symmetric to a casual observer. However, they are still asymmetric both externally & internally. On the outside, the breathing hole, anus & the genital opening are all on the right side of the head (in dextral individuals). On the inside, the genitalia & the intestines are distributed throughout the body asymmetrically.

I think organisms such as the amoeba, mycoplasmas, and phytoplasmas are without symmetry.  And many plants are asymmetrical, although their idividual parts may be symmetrical those parts are arrange asymmetrically.