Seems fairly common that a bunch of the A-listers take a memento or two, but apparently the studios have some pretty strict rules about it bc everytime you see an interview about the topic, almost every actor is pretty shocked they have what they have or are pretty sheepish about it. It also seems like the mementos are either completely random, or something where there were multiple being used. So while common, i dont think the studios like when they take certain things.
I read Chris Hemsworth has taken a prop Mjolnir from each Thor and Avengers film. I'm sure there were a ton though. just like Daniel Radcliff supposedly kept a couple sets of Harry Potters glasses from filming, but again, im sure there were multiple. Rupert Grint supposedly swiped the golden egg from The Goble of Fire but the studio made him give it back so clearly there is a line and/or certain things the studios refuse to let the actors keep.