[TimM]

My favorite so far:

This is Armenian Radio; our listeners asked us: “Why Lenin wore regular shoes, but Stalin wore boots?”
We’re answering: “At Lenin's time, Russia was still only ankle-high in [censored].”


I found the site searching for this joke:

A Polish tourist comes back home after visiting the USSR. He carries two very large and heavy suitcases. On his wrist is a new Soviet-made watch. He tells the customs man: "This is a new Soviet watch. It's a wonder unknown in the capitalist countries. You see, it shows time, the rate of your pulse beats, the phases of the Moon, the weather in Warsaw, Moscow, and New York, and more and more!"

"Yes, it's a wonder," the customs man agrees. "And what is it you have in these big suitcases?"

"Oh, it's just the batteries for the watch."