If every person on the planet generates a new UUID4 every second, we’d expect a collision to occur after about 10 years.
UUID4 is the commonly-used variant of the UUID spec that uses randomly generated numbers to choose the UUID instead of information about the generating machine or what have you. UUID4’s leave 122 of the 128 bits available for random data, which by the birthday paradox means we should expect a collision after about 2^(122/2) have been generated. That’s 10^18.4 about. The earth has about 10^9.9 people in it, and a year has almost exactly 10^7.5 seconds in it.
9.9+7.5 = 17.4
10^(18.4–17.4) = 10
So about 10 years.
It’s extremely unlikely there have been any collisions for properly generated UUID’s so far. (But buggy code has certainly generated collisions.) However, as we look to the not-so-distant future where everybody is generating data all the time, it’s clear we’re going to need more than 128 bits for our UUID space.