I believe "I think therefore I am" is better worded as; "I have original thought therefore I am."
Original thought is the proof of existence. Think of something that is totally and completely yours and you will have proven your own existence. Unfortunately, as others have said on this thread, you can only prove your existence to yourself. That being said, I can prove that I am or am not a figment of your imagination simply by being at your funeral.
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Round and round the shutter'd Square
I stroll'd with the Devil's Arm in mine
No sound but the scrape of his hoofs was there,
And the ring of his laughter and mine.
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