It's never a problem in Europe.

BUT, I've had a 5 year nightmare entering the US because one of those green visa waiver stubs was lost in 1997 (it was collected, but never made it to the relevant authority)...so they (not so) naturally assume I overstayed. This actually happened more than once, but I was able to prove I'd left every other time because of the diligence of the Australian entry points of always stamping my passport. Because I left the US for the UK that time, and the UK never stamp UK passports, I wasn't easily able to prove I hadn't overstayed.

It took obtaining a visa to finally sort it out, and I'll apparently have to always have a visa now to enter the US. Very annoying.