Yes, obviously this sort of information tends to be classified indefinitely but especially with defectors we often know that they were spies beforehand, here's some examples:
http://en.wikipedia.org/wiki/Ryszard_Kukli%C5%84ski http://en.wikipedia.org/wiki/Arkady_Shevchenko http://en.wikipedia.org/wiki/Michael_Goleniewski http://en.wikipedia.org/wiki/Oleg_Gordievsky (spied for the UK)
edit: you can get further examples from people that we know were betrayed by double agents like Aldrich Ames and Robert Hannsen, for example these: http://en.wikipedia.org/wiki/Aldrich_Ames#Some_CIA_sources_betrayed
Oleg Penkovsky (alongside Oleg Gordievsky and Vasili Mitrokhin, both of whom spied for the UK and later defected) was one of the most senior Soviet agents the Anglo-American intelligence services ever managed to recruit; he fed intelligence to the CIA for three years from his position as a colonel in the GRU (Soviet military intelligence), before being blown and almost certainly executed.
Penkovsky is hugely important in terms of intelligence history (and 20th century history more generally) because he supplied Langley with the intelligence that predicated the Cuban Missile Crisis — specifically, that the USSR was in the process of placing nuclear weapons on Cuba.
There's a lot more to be written on this — both the UK and US had hugely active intelligence operations in the USSR for decades. I'm pretty sure a more open society, judicial system and press in the west is the root of the popular perception that it was a one-sided fight, but there's also the fact that the KGB and GRU were masters of, and heavily reliant upon, HUMINT as their primary intelligence collection method. The US/UK intelligence establishments had more diversified collection systems, particularly in terms of bigger and more technologically advanced SIGINT operations.
I'm at work right now, but will try and come back later and write more. Apologies also for scarcity of sources — same reason!
Ever heard of the U-2 incident? Look it up, we were trying to spy on the soviets and this crisis happened which increased tensions.