The former Soviet flag, which I'm sorry to admit looked cooler than the modern Russian flag.
The cold war. Never understood why the Americans and the Russians had to be such bitter enemies. But then again, why do we have to be enemies with any country?
Boris Badenov and Natasha Fatale. Although according to the Rocky and Bullwinkle cartoon they came from a fictional country called Potsylvania where everyone is comically evil.
Jokes that go, "In Soviet Russia, something-something YOU!"
The stereotype that Russians are always serious and never smile. It's not really that, it's just that they don't see people who smile when greeting you for the first time as being friendly or polite. Instead they see it as fake or even threatening. "The American smile".
The "Husky Rusky" stereotype with the furry hats with big flaps.
The nesting dolls. I still remember that cute sketch on Sesame Street that used stop-motion animation while counting them. And one of them saying "wrong way, dummy".
Baba Yaga. She's a witch or an ogress from Russian folklore, and she lived inside a house that had giant bird legs that would walk around, she flew on a giant pestle instead of a broomstick, and she was know to eat bad little Russian children. Or threaten to, unless they fetch an item of some kind.
The cartoon "Nu! Pogodi!" It was sort of a Russian version of Tom and Jerry, where the protagonist is a Hare, who had to deal with a Wolf, who wants to catch and (presumably) eat him. You don't really need to know Russian to watch the cartoons since there's very little dialogue, and most of the humor comes from Wolf. The cartoons would often, but not always, end with Wolf saying "Nu! Pugodi!" which translates to roughly something like "I'll get you yet, wait and see!"
And the pirated game "Wait and See" based (very loosely) on the cartoon. Not only is it terrible and nearly impossible to finish, but the game over screen is just beyond disturbing, where it shows Wolf snatching and swallowing up Hare (neither of them look the way they do in the cartoon, they instead look like bad imitations of Wile E. Coyote and Bugs Bunny), and then pointing at and taunting the player.
Wintery weather.
The Nutcracker and Sleeping Beauty ballet by Tchaikovsky. He really hated the Nutcracker ballet, even though it turned out be the most popular thing he ever wrote, according to Disney's first Fantasia movie. I like the music and all, especially the Dance of The Sugar Plum Fairy, but those nutcracker doll ornaments my mom likes to put out at Christmas are just plain creepy! Which is probably why she likes them so much.
The Sputnik 1 satellite, the first to be launched into space. While the Americans clearly did the Moon Landing so they wouldn't be outdone, I don't believe the whole thing was nothing but a hoax, especially after seeing it done on Mythbusters.
Zangief from Street Fighter 2. The American ports of the game tried to make him look like a totally evil commie, although in the Japanese version he was something more of a gentle giant (when he wasn't violently pummeling another Street Fighter's brains out). Around the time the arcade game came out, however, the Cold War was ending (although things elsewhere were definitely heating up, if you pardon the pun).
An earlier game, Missile Command. Although the backstory was that you were trying to protect the planet from an invasion of space aliens, the Cold War influence was unmistakable, and it used to really creep me out as a kid. The arcade version of the game would say THE END instead of the usual GAME OVER, implying we've all been nuked.
The song "99 Red Balloons". The original German version of the song that was really popular in the eighties sounded fun and lighthearted, but its dark Cold War overtones were lost on many non-German-speaking people. It's about a couple of kids who released a bunch of red balloons into the sky just for the fun of it, but it gets mistaken for a soviet threat and nuclear war ensues. I have the English version on CD. You really get the message when you hear it, especially near the end.