White Sun of the Desert (Vladimir Motyl) … well, this one isn’t technically a comedy, but it’s not entirely serious, either. Plenty of comedic elements, certainly.
Animation:
Town Musicians of Bremen (YouTube links at the TV Tropes link. Bonus: if you’ve seen almost any of Gaidai’s films, you’ll find a certain trio of characters in this one to be quite familiar…)
Karlsson-on-the-Roof (Adaptation of a series of children’s books by Astrid Lindgren)
Additional recommendations (no YouTube links, sorry—maybe others can find some):
Gentlemen of Fortune (Daneliya)
Operation Y and Shurik’s Other Adventures (Gaidai)
White Sun of the Desert (Vladimir Motyl) … well, this one isn’t technically a comedy, but it’s not entirely serious, either. Plenty of comedic elements, certainly.
Animation:
Town Musicians of Bremen (YouTube links at the TV Tropes link. Bonus: if you’ve seen almost any of Gaidai’s films, you’ll find a certain trio of characters in this one to be quite familiar…)
Karlsson-on-the-Roof (Adaptation of a series of children’s books by Astrid Lindgren)