Googol: 10^{100}.
Written out, this would be the digit '1' followed
by a hundred zeroes.
This is big — for context, the # of particles in the
universe (electrons, photons, quarks, etc),
is estimated at 10^{80}.
So a googol is 10^{20} (100 quintillion) times bigger.
That is, if you went around the entire universe,
and for every sub-atomic
particle you stopped and counted up to a quintillion, then you'd only
be 1% of the way to a googol.
In the late 1930s, [mathematician Edward Kasner] was once asked to come up with a name for a very large number. He outsourced this task to his nine-year-old nephew, Milton Sirotta, who in turn coined the word ``googol''.
Googolplex: 10^{google}.
A number of interest only to theoreticians.
It has a googol (and one) digits —
so even if you just try to write the number
down,
and you could somehow inscribe a quintillion (10^{18}) digits onto
every particle in the universe, you'd only write down 1% of all the digits
(and thus your written number would merely be one googol'th of a googolplex).
Google: A company whose name, according to answers.com, …
… started as a joke boasting about the amount of information the search-engine would be able to search. It was originally named 'Googol', a word for the number represented by 1 followed by 100 zeros. After founders Stanford graduate students Sergey Brin and Larry Page presented their project to an angel investor, they received a cheque made out to 'Google'
Googleplex:
Silicon Valleyism for Google's new headquarters/campus.
(Originally built for SGI back in it's heyday.)
Gogol, Nikolai: The Russian playwright's name is spelled (and pronounced) differently yet.