After careful finetuning of my search string, I've concluded the highest number Google can stomach is somewhere around 1.79769313 × 10308.

How did I get this number?

Well, the equation grew organically: Siliziumleben posted his results for teaspoons in a cubic lightyear. Then femtoliters in a cubic megaparsec. I upped the ante to femtoliters in a cubic teraparsec, but there was still room. I had to figure out how far up and down in the naming of multiples of a thousand google can go.

Turns out it's yotta (1024) in the > inf direction and yocto (10-24) for values approaching zero. So, there I was with yoctoliters in a cubic yottaparsec. By that time, it had become less a race of getting the most outlandish units to clash and more of a race for the highest number Google could produce. I added multipliers to push beyond 10300, and finally found a brick wall. Google would tell me that there were infinitely many cubic yoctometers in (18 !) times googol (cubic yottaParsecs). The rest, as they say, is history!

Here's the exact search string that I ended up using:

((12.2444329202069885 * (16 !)) + (17 !)) times 1 googol (cubic yottaParsecs) = 1.79769313 × 10308 cubic yoctometers

Extending the 12.24somethingsomething multiplier beyond 16 digits of the fraction is left to the reader as an exercise : )

Update: I have been informed that Google works with 64Bit numbers, and that the highest number Google can deal with is therefore 2^(2^64) - 1. While you can't plug that into Google Calculator (the intermediate result 2^1024 is too large to handle), you can approximate it with (2^1023) * 1.999999999999999 = 1.79769313 × 10308.