If you generate 1 billion UUIDv4s a second, it would take, on average, 85 years for you to produce a duplicate, and the resulting list of UUIDs would take up ~45 exabytes. And keep in mind that even if inserting a row fails because you've somehow managed to generate a duplicate UUID, it is trivial to make a new UUID and retry. Since the database enforces the uniqueness constraints of primary keys, I'm hard pressed to come up with a scenario in which generating a duplicate UUID would actually do anything serious.

GP pointed out the special version of the algorithm that handles collisions gracefully. Note that this algorithm ("open addressing") is so frequently used that you will probably find a variation of it in pretty much any piece of software you have ever used. It's a well-understood method, not only from a practical perspective but also in terms of theory; check out e.g.: https://en.wikipedia.org/wiki/Linear_probing