The definition of 'Karma' is simply action. Everything we do is karma. The concept of karma, however is the law of cause and effect. Each action results in some kind of effect. Taking that further, everything we do will not only affect others, but will have an effect on us, as well. So, any positive actions will have a postive result and any negative action will have a negative result, which will affect us in return at any given point.
Do I believe in karma? Yes. For several reasons. First, because I've taught yoga for years and studied hinduism. LOL. Second, because everything we do is held within our psyche, which later may cause us to preform actions to bring actions full circle. This is kinda the idea behind positive thinking producing amazing results. Third, sometimes past actions are not forgotten by other people and they may later pay us back for positive or negative actions.
The esoteric idea of karma resulting in future circumstances is a little questionable, but maybe not entirely. I've certainly had some interesting, seemingly unrelated things bring things back into balance. I've even had my past actions played back to me by someone entirely different. Wild! However, when one gets into the idea of coming back as a frog, then it's dipping into the belief of reincarnation and not necessarily karma. Though reincarnation teeters on the same premise that life is cyclic and past actions, even in another life, must still be resolved, one must not necessarily believe in it to believe in the law of karma.
By the way, according to yoga, positive actions have the power to 'burn' negative karma so one does not necessarily have to suffer the consequences.