I came acorss this discussion when I was looking up some information about Hindusim and I thought it was interesting for it is not something I have before given active thought to, but I am inclined to beleive that animals do have karma.
For one thing, in both Buddisim and Hindiusim animals take part in the act of reincarnation just as humans do, and in theses systems, Karma is seen as having an influence in the reincarnation process, and so if animals are reiencaranted, and karma is a part of reincarnation then they should have karma of thier own.
Also, karma is something that is attachted to a soul or spirit of person, which is why it can follow them, or affect them from one life to the next, so in my beleif that all living things have souls, then animals just as well should have karma if they also have a soul.
Karma in the eastren traditions is about duty and one following thier duty. It one lives by thier duty they aquire good karma, if they do not follow thier duty they aqcuire bad karma, and though animals live by a different set of rules then people do, they still have thier place, and thier roles, and thier own duty to follow.