Here are a couple of memes that have made the rounds of the Runet (Russian Internet).
In this video, which went viral a couple of years ago, Медведев (President in this video, now Prime Minister of Russia) is caught dancing at a private function attended by, among others, Иван Ургант (a popular television personality):
Язь - рыба моей мечты! This video of a Russian man very excited at his big catch has spawned parodies and remixes. Язь = ide or orfe, a type of fish. Here is a brief description of the meme in English from Know Your Meme.
The Russian ska punk band Ленинград referenced this meme in a recent song:
This link on the Cornell University Russian site takes you to several very short, very entertaining videos from a popular Russian TV humor program. Though you probably won't be able to understand them all, you should be able to get some of the humor; transcripts and glossaries are provided for extra help.
Watch this home video that singer/songwriter Олег Лёгкии made for his grandparents (his бабушa is holding the camera, and his дедушка comes home in the middle and seemingly ignores the whole thing). He even sings some songs in English.