One of the biggest numbers that actually applies to something: Graham's number.

There is no highest number. Given any number, we can easily think of a higher one. But this number is actually higher than any number I've ever thought of before. Using scientific notation, there would not be enough room in the universe to write it. It is higher than the number of particles in the universe, than the number of seconds since our universe began, etc. Despite being inconceivably large, it doesn't end with a string of zeros; the last ten digits of Graham's number are "2464195387"--I almost want to dial that number into my phone... apparently it's in Barbados...

Graham's number can only be written using Knuth's up-arrow notation, which is pretty cool in itself. Graham's number was popularized in the 1980 Guiness Book of World Records, although according to Wikipedia, "specific integers known to be far larger than Graham's number have since appeared in many serious mathematical proofs."

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