The Soviet Union for nearly a century was the 'other' Superpower; the counter to American military might around the globe. The Soviets made numerous military accomplishments and even today Soviet Technology is still in use both for military as well as non-military uses; including tourism.
The most commonly known Soviet Weapon is probably the AK-47, named for designer Mihail Kalshnikov. The Kalashnikov is known not for it's accuracy but it's resiliency on the battlefield, and extremely simple parts. This is one reason it remains popular among terrorist groups in underdeveloped nations where precision parts are hard to come by.
Another popular Soviet weapon is the Katyusha rocket. Named after a cute nickname for a woman named Ekaterina, or Kate, these are far from cute. While relatively aging, the fact that these can be fired from essentially something the size of a pickup truck has made them a favorite of terrorists.
Soviet nuclear technology was extremely formidable and remains key to Russian Federation defense today. The most powerful ballistic missile of all time was the RS-20, or SS-18 called 'Satan' in foreign language documents; no anti-missile defense can counter it. President Obama is working with Russian President Dmitry Mdvedev to mutually reduce Nuclear weapons. The Russians however are still actively developing weapons to counter anti-missile systems, and bringing weapons like the RS-20 back into service.
Some Soviet technology has been put to use for good. The Il-76 cargo plane has been successfully used for fighting fires. California has considered using the Ilyushin in fighting fires. In recent fires in Greece the Ilyushin was heavily used.
While the Soviets made many accomplishments themselves not all were Soviet Innovation. The KGB may not have managed to have surveillance camera systems in every apartment building, and in fact relied little on surveillance video, but certainly aide in acquiring new technologies to keep the Soviet Military strong. The now declassified transcripts of the Venona Project show that when communism's lack of a free market did not produce results the Soviets were able to borrow technological advancements from their neighbors.
While the Soviet Union has come and gone the advancements of Soviet Technology are still being built on today. Russia has successfully tested missiles that can evade missile defense based on Soviet Designs. Also Soviet era stealth technology programs are being realized in the Sukhoi T-50. Russia is building upon legacy Soviet Military Technology for the future.