The matroshka, commonly called the "nesting doll," is easily the most identifiable bit of Russian culture to foreigners. Open one, and you'll find another inside through many layers. They can be a few inches or several feet tall. If you go to Russia and leave without one, fire your guide.
A popular folk instrument in Russia at least as far back as the late 1600s is the balalaika. They tend to have two to six (but usually three) strings, a triangular body, and a short stem. It likely evolved from the Mongolian Dombra, which had an oval body and longer stem, that was introduced to Russia during the Mongol occupation.
The ushanka, literally: ear-flaps-hat, is a traditional Russian hat. The ear flaps can be tied over the top, under the chin, or simply left hanging.
You've seen it in movies or pictures of Russian folk dances, but the kazachok is still popular today at get-togethers. In fact if you hang out with us often enough, you'll get to do it too!
The name comes from the Cossacks, kazaki, who invented the dance, but it is also known by other names among the many Slavic groups that enjoy it. Thanks to the Russian Program at Purdue University for the neat illustration!