To me karma isn't just a spiritual philosophy but a basic principle of life. Every action has a consequence. If you do bad things, bad things come back to you. If you do good things, good things come back to you. The same is true of thoughts - dwelling on the negative only brings the negative to you, and vice versa. Anyone who disputes karma is simply being ridiculous.
I, as a Buddhist, believe that karma follows one's soul through each incarnation. If one has committed a gross karmic action (let's say rape), they will then suffer in the next life and the purpose of that life will be to learn about the true difference between morality and immorality.
It is important to note that not ALL suffering is the result of immoral action (which I define as unnecessary harm to another). For example - the death of a loved one and the trauma that you experience afterward doesn't necessarily occur because you committed murder in a past life. There are some things we are not meant to know -s uch as what we have done wrong in a past life and what we are meant to learn in the current one.
Thus, suffering is basically inevitable either as a result of unfortunate circumstances or because of past actions. However, it is not un-conquerable (is that a word?

). The best we can do is attempt to curb our desires in order to alleviate suffering and in the process we learn the nature of life, knowledge, happiness and morality.
Karma is what spurs the process of learning. The purpose of the journey of reincarnation is to constantly learn and take away from each life new knowledge about the nature of both your soul and the universe around you.
As for karma being threefold? I dunno. I think the measure of the consequences one actually experiences due to an action depends upon the environment. I don't think it is a universal law that karma works threefold, but I don't dispute that it does occasionally.
*steps off soapbox*