Largest number in ten bytes of code
Perl, >1.96835797883262e+18

time*time


Might not be the largest answer... today! But wait enough millennia and it will be!

Edit:

To address some of the comments, by "enough millenia," I do in fact mean n100s of years.

To be fair, if the big freeze/heat death of the universe is how the universe will end (estimated to occur ~10100 years), the "final" value would be ~10214, which is certainly much less than some of the other responses (though, "random quantum fluctuations or quantum tunneling can produce another Big Bang in 101056 years"). If we take a more optimistic approach (e.g. a cyclic or multiverse model), then time will go on infinitely, and so some day in some universe, on some high-bit architecture, the answer would exceed some of the others.

On the other hand, as pointed out, time is indeed limited by the size of integer/long, so in reality something like ~0 would always produce a larger number than time (i.e. the max time supported by the architecture).

This wasn't the most serious answer, but I hope you guys enjoyed it!