I have just read Ben MacIntyre’s superb “Double Cross:  The True Story of the D-Day Spies” (Bloomsbury, London 2012), which describes the succesful counter-espionage operation conducted by the British against the Nazis in Britain during WW II.  Every Nazi foreign agent in Britain was captured and either tried and executed, or turned, being run by the so-called Twenty (“XX”) Committee.  This network of double agents, many of whom created fictional sub-agents, became a secret weapon of considerable power, able to mislead and misdirect  Nazi war efforts through their messages back to their German controllers (in France, Portugal, Spain and Germany).
The success of these misdirections was known precisely, since Britain was able to read most German encrypted communications, through the work of Bletchley Park (the Enigma project).  Indeed, since the various German intelligence controllers often simply passed on the messages they received from their believed-agents in Britain verbatim (ie, without any summarization or editing),  these message helped the decoders decipher each German daily cypher code:  the decoders had both the original message sent from Britain and its encrypted version communicated between German intelligence offices in (say) Lisbon and Berlin.
This secret weapon was used most famously to deflect Nazi attentions from the true site of the D-Day landings in France.  So successful was this, with entire fictional armies created and reported on in South East England and in Scotland (for purported attacks on Calais in France and on Norway), that even after the war’s end, former Nazi military leaders talked about the non-use by allies of these vast forces, still not realizing the fiction.
One interesting question is the extent to which parts of German intelligence were witting or even complicit in this deception.  The Abwehr, the German military intelligence organization, under its leader Admiral Wilhelm Canaris (who led it 1935-1944), was notoriously anti-Nazi.  Indeed, many of its members were arrested for plotting against Hitler.  Certainly, if not witting or complicit, many of its staff were financially corrupt, and happy to take a percentage of payments made to agents they knew or suspected to be fictional.
Another fascinating issue is when it may not be good to know something:  One Abwehr officer, Johnny Jebsen, remained with them while secretly talking to the British about defecting.   The British could not, of course, know where his true loyalties lay while he remained with the Abwehr.   Despite their best efforts to stop him, he told them of all the German secret agents then working in Britain.  They tried to stop him because once he told them, he knew that they knew who the Germans believed their agents to be.  Their subsequent reactions to having this knowledge  – arrest each agent or leave the agent in place – would thus tell him which agents were really working for the Nazis and which were in fact double agents.
Jebsen was drugged and forcibly returned to Germany by the Abwehr (apparently, to pre-empt him being arrested by the SS and thus creating an excuse for the closure of the Abwehr), and then was tortured, sent to a concentration camp, and probably murdered by the Nazis.  It seems he did not reveal anything of what he knew about the British deceptions, and withstood the torture very bravely.  MacIntyre rightly admires him as one of the unsung heroes of this story.
Had Jebsen been able to defect to Britain, as others did, the British would have faced the same quandary that later confronted both CIA and KGB with each defecting espionage agent during the Cold War:  Is this person a genuine defector or a plant by the other side?  I have talked before about some of the issues for what to believe, what to pretend to believe, and what to do in the case of KGB defector (and IMHO likely plant) Yuri Nosenko, here and here.