From the 2010 New Year's TV special Оливье-Шоу ("Olivier" here means the Russian-style potato salad traditionally eaten as a New Year's dish). This computer-animated "кукла" caricature of Obama also appears regularly on the show Мульт Личности.

Йааа гаварыт оучинъ карашо парюски!

Anyway, this clip provides a funny example of someone speaking Russian grammatically but with a VERY heavy American-English accent. One could easily believe that it was done by an American actor reading lines that were written phonetically -- "YAH pahz-druhv-lee-YAH-oo VAHSS", etc. -- until the very last line. (Произношение английской фразы "Хэппи Ню Йир" совершенно выдает актера за русским.) In other words, if your spoken Russian sounds anything close to this, you need a lot more work to improve your pronunciation, lest you remind people of Sean Connery in The Hunt for Red October.

Sorry that I couldn't find a version on YouTube with English subtitles, but it's not too difficult to understand. (If any of the native Russian speakers can provide a transcript of the text по-русски, I would be grateful -- there are just a few words that I can't catch.)

ЗЫ Another clip from Мульт Личности, with Barack Obama and Hillary Clinton. "Хилари" also speaks Russian with an American accent, though hers is less ridiculous-sounding than what we hear from "Барак".