Duck Soup, with Harpo Marx imitating Groucho. Harpo did a reprise of this with Lucy in I Love Lucy.
In one of the Hot Shots! movies, Charlie Sheen is on a Vietnam-era patrol boat, doing a voiceover as he writes in his journal, just like in Apocalypse Now. Another voiceover intrudes, saying the same words, and another patrol boat approaches them going in the opposite direction, and you see Martin Sheen is in that one.
They each stand, stare at each other, and as the boats pass, they shout at each other, “I loved you in Wall Street!”
I really loved Helena Bonham Carter as Hermione Granger in Harry Potter 7.1 - wonderfully awkward!
I heard that they first shot Emma Watson doing the scene so that Helena Bonham Carter could get the mannerisms down perfectly.
I don’t know if it aired in the US yet, but there’s an episode of Lost Girl where the entire main cast swaps bodies. Kenzi gets Dyson’s body and I think Kris Holden-Reid does a pretty funny, spot-on imitation of Ksenia Solo. (off the subject, but man that little goth pixie is smokin.)
There’s a Laurel & Hardy short where a blood transfusion goes wrong, and they each end up acting like the other one.
Probably Thicker Than Water, 1935
HBC did such a really fantastic job of that. When she showed up on screen my brain instantly recognized her as “Hermione in a Bellatrix costume” without even stopping at “EEEk, Run! Bellatrix!”
In the deleted scenes for In Bruges, Matt Smith does an excellent Ralph Fiennes. Highly recommended.