This actually happened to me a few months ago in Venice, except that it was a credit card in a water taxi ticket machine. I was so relieved to have my tweezers on me, I just pulled that sucker out. Otherwise, I would have been up a creek without a paddle.
Sometimes your card will get stuck because the machine is old and crusty, other times it's because thieves put a sticky substance or a plastic insert into the slot, intentionally to trap your card -- then after you've thrown your hands up and given your card up for lost, they come back later with their own pair of tweezers to empty their traps. Bottom line, it's small and totally worth it to put in your bag!