Although it may be argued that bacteria are symmetrical (no, not perfectly, but the way that the term is used in biology they may be considered symmetrical), it is certainly fair to point out that symmetry is nowhere near universal among living things. That being said, bilateral symmetry is certainly the rule among motile animals (of course this includes many familiar animals, and is likely what the OP was referring to). It is developmentally simple to have one side a mirror image of the other side (or nearly so), but I would argue that the reason for this pattern is related to the motility (note that this pattern virtually disappears when we look at animals that are not motile, or at plants or fungi). Obviously if you are moving there are some things you would like to have at your front and other things you would like to have at your rear. Perhaps less obviously there are some things you would like to have on your bottom and other things you would like to have on your top. However, under most circumstances you want the same things on your right side as you do on your left side. In addition, being symmetrical makes locomotion much easier (e.g., it ensures that drag is similar on each side).
Peez