For ex, one story had a woman who told the tragic tale of how a prophecy said she'd marry her son, so she stabbed him and left him for dead, only to have him found by a villager who saved him, and many years later this young man came to her asking for her hand, and only after they'd been married did she see his scar and realize who he was.
There's also a story about a girl who is sent off by her rich father when she doesn't give him the answer his pride desires (very similar to the princess who brings her father the king a gift of salt). And a story about a beautiful girl who catches the attention of a prince, only to have her aunt connive to put her cousin in her place, but the girl accepts her lot and is able to reclaim the prince anyway (very similar to the story of the princess whose servant forces her to switch places with her on the way to the prince). And a story of three princes sent out to do a nearly impossible task, which only the younger succeeds in, so the elder two conspire to take his glory, but of course he is able to outwit them in the end (which I've seen in a few different stories from various cultures). Naturally there are often three sons or daughters, and the youngest is almost always the wisest and most successful. The help of beasts and monsters can be won through simple kindness.
Of course, there are many differences as well--there's a lot about cousins being betrothed to each other by right, and much to do with camels--but it's amazing how many similarities there are. I haven't studied comparative mythology enough to know the theories on why this is, whether it's themes that just seem to resonate with humans in general, or whether stories have passed from culture to culture and evolved. But either way, how fascinating!