I'd add that it's also used when data is created in multiple places.

Consider say weather hardware. 5 stations all feeding into a central database. They're all creating rows and uploading them. Using sequential integers for that is unnecessarily complex (if even possible.)

Given the amount of data created on phones and tablets, this affects more situations than first assumed.

It's also very helpful in export / edit / update situations. If I export a subset of the data (let's say to Excel), the user can edit all the other columns and I can safely import the result. With integer they might change the ID field (which would be bad). With uuid they can change it, but I can ignore that row (or the whole file) because what they changed it to will be invalid.