I don't really have much time so I will add stuff little by little. For the same reason, some things here are just from the top of my head so comments with links and resources that support them will be appreciated.
 

Impression that majority of the foreigners have about Russia is mostly built on myths and stereotypes that are as close to the reality as the Baywatch to a lifeguard's manual. Cold War propaganda was bad but what even worse - it doesn't stop. If they don't do it to create an image of the enemy, they do it to make newspaper articles more sexy. I will not educate you or try to convince you. I'll give you some facts and let you think. Often, it's more than enough just step inside of a stereotype to make it disappear. So:

1. It is very cold in Russia.

Russia is big. This is Russia and this is Russia. If someone say that the US is very hot it will be a true statement about Arizona and false one about Alaska. Here you can find a map and some facts.
 

2. It is always cold in Siberia.

Siberia is big - see previous answer. The coldest place of the Northern hemisphere is located on the north of Siberia and it is cold, once every few years they have like -65C°  or so. The other parts are different, for example the part where I was born, has continental climate which means it is dry, relatively cold during the winter  ( -20C° is an average, people from Alaska will laugh) and hot during the summer - I think June - July average was like 25-30C° (80 - 90F). Besides, strong winds are not typical for continental climate so it's easier in winter.
 

3. Only criminals live in Siberia.

I used to answer: Yes, and in Australia too. Actually, if you look little bit farther back in the history, in the North American Colonies, too. Today, well, obviously, there are some correctional facilities - and any state in the US has them too. More...
 

4. Russian mafia is everywhere or All Russians are mafia.

What do you think? Let me know. My answer will be here shortly.
 

5. I know Russia - I spent two weeks in Moscow

Yes, of course. It's like one of these Soviet journalists who would come in the US, spend a week or so in NYC, going to a number of places that government of the Soviet Union deemed to be "safe" and "appropriate", with a guide from a tourist agency that was deemed "reliable",  then come back to Russia and write a book  "America from A to Z".

6. Russian names (both first and last) are very long and impossible to pronounce

Tanya (or Ivan) is a typical Russian first name. Smirnoff ( I'd write Smirnov) is a typical Russian last name. Goggentcollern and Quantishishvilly are NOT Russian names. Any questions? More...

7. If I go to Russia there will be a KGB agent following me everywhere.

(answer by 007 - translation by SVD) Sorry to disappoint you but, most likely, not. Surveillance, especially surveillance by a human (as we call it "leading" ) is extremely expensive and complicated technique and is rarely used by KGB (FSB, as it called now) and only if we have very serious grounds to believe that the "object" is involved in terrorism or other anti-state activities. During the "Cold War" KGB might be checking on somebody "just in case", (analogous US agencies did the same) but nowadays, given the number of foreigners coming to Russia everyday to be followed you'd have to be actually involved in criminal activities or have your passport photo taken in one of Bin Laden' s camps, with appropriate background. That's a joke.

8. Vodka as Russian national food

What do you think? Let me know. My answer will be here shortly.

9. Russians are lazy

What do you think? Let me know. My answer will be here shortly.