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I'm intrigued by the concept of Koans. From my understanding, excessive effort in contemplating the impossible leads to letting go of thinking of things in a logical, cyclical and worldly manner, and aids the process of achieving enlightenment. If I'm not quite right in this definition, let me know.

I'm particularly interested in learning different koans that are out there. the only ones I know are "What is the sound of one hand clapping?" which I believe is Zen, "How many angels can fit on the head of a pin?" which is Christian, and "If a tree falls in the forest and no one's around to hear it, does it make a sound?"... and I'm not sure what tradition that last one is from.

Anybody got any other koans that I can attempt to wrap my mind around?

A koan is any form of question, story, poem, etc. which cannot be resolved or understood through conventional wisdom. However, when a non-dual perspective is applied, the apparent paradoxes in the situation are resolved. These resolutions cannot be stated in linguistic terms, nor can the method of "solving" a koan. Hence, the contemplation of and meditation on a koan is an act in applying the religious, non-dual perspective to an actual idea or situation.

My personal favorite is:
"Joshu asked Nansen: `What is the path?'
Nansen said: `Everyday life is the path.'
Joshu asked: `Can it be studied?'
Nansen said: `If you try to study, you will be far away from it.'
Joshu asked: `If I do not study, how can I know it is the path?'

Nansen said: `The path does not belong to the perception world, neither does it belong to the nonperception world. Cognition is a delusion and noncognition is senseless. If you want to reach the true path beyond doubt, place yourself in the same freedom as sky. You name it neither good nor not-good.'
At these words Joshu was enlightened."