Someone wanted to see a post about cultural differences between these two "superpowers"...
From my own experience, cultural differences should never be underestimated in their importance. You can learn to speak a language, even fluently, but if you do not understand the culture that the language grew out of, you will never really be "fluent" in that language.
I have lived in both countries and here are some of the cultural differences I have noticed (and some I have learned the "hard" way):
Personal space. Americans prefer a lot more personal space than Russians do. In Russia, people are comfortable talking with maybe a foot of personal space between them, whereas Americans prefer closer to three feet. Americans are very uncomfortable with "close talkers" so if they start to back away when you are talking, don't close in on them.
Repeating "I'm sorry" or "thank you" or pretty much anything will make you look like you can't be trusted in Russian culture. So, apologize once or say thank you once, and then let your actions show that you mean it. Repeating the same words to emphasize them will hurt your credibility.
Trust and openness. Americans may seem very open at first, but in reality it can take a very long time to earn an American's trust. Americans can even become close friends, and then disappear suddenly from your life. This is hard for Russians to understand because they value their connections and friendships a great deal, perhaps more than Americans who are used to moving away from family and friends as a part of our lifestyle.
Dating. In Russia, men are expected to pay for all of a woman's expenses when they are on a date. If you offer to "dutch treat" this can be very offensive, like saying that you don't think he can afford it. Times are a-changing, so this may not be as big of a deal as it once was. But "feminism" is still frowned on by a majority of people in Russia. Russians prefer women to dress attractively and men are expected to open doors, carry your bags or luggage, and give up seats for women on public transportation. They are not doing this to "control" you - they are doing it out of respect. So just go with it and enjoy!
In America, it's quite common for men and women to share the bill on a first date. Also, dressing standards in America seem "poor" to many Russians who do not understand "Wal*Mart People".
If you are in Russia, it is extremely unwise to call someone "comrade" or "commie" or even "russki" (even though that is the Russian word for Russian).
That's all I can come up with on one cup of coffee. Please feel free to add your own observations!!! I know there is a LOT I have left out and it would help me to learn more as well.