I have been watching the series [The Americans](http://en.wikipedia.org/wiki/The_Americans_(2013_TV_series). I was wondering how much of that show actually represents what occurred in the Cold War period? Were Russians really spying or have the capability to spy on US soil in the 1980s? Are the tactics that the spies use in this show realistic?
The closet RL thing to the sort of deep cover illegal that is historically known to have taken place was the KGB agent Konon Molody, aka Gordon Lonsdale. Molody was stationed in London during the 1950s.
The main difference between Lonsdale and the TV Americans is that while the identities that Philip and Elizabeth use seem to be made from whole cloth, 'Gordon Lonsdale' was a real person - a Canadian citizen of partial Finnish descent, born in Cobalt, ON but taken back to Finland by his mother at a young age after a messy divorce. It's presumed Lonsdale died during WW2 and the Soviets got hold of his identity when they captured some Finnish government records.
Molody emigrated to Canada where he assumed Lonsdale's identity, legitimately acquiring Canadian documents, and then moved to London, where he was the KGB's senior illegal operative, passing himself off as a Canadian expat. Like Phillip and Elizabeth he was a businessman whose work required him to travel (he owned and rented amusement machines).
Another interesting case, ironically a bit different from Phillip and Elizabeth but in some cases even more successful, was Iosif Grigulevich, a Soviet citizen of Crimean ethnicity who grew up in Argentina. Relocating to Europe he managed to acquire a Costa Rican passport in a fictional identity and was so successful in ingratiating himself with he Costa Rican government that he was appointed Costa Rican ambassador to Italy!
So, short answer, yes, the KGB was able to implant operatives in other countries who passed themselves off as natives. Did they do this in the USA itself? There are no confirmed cases, but it seems within the realm of plausibility.
While it is a fictional television show made to entertain, not educate, and pretty much everything seen should be taken with a grain of salt, it does have a few bits and pieces that are based on reality. Joe Weisberg (the shows creator) was a CIA officer at one point, and it does appear he's added some bits to the shows story line that help give some basis of reality to some of the plot points.
For one, the show shows the two KGB lead characters often resorting to using the "Honey Pot" tactic (using sex and emotional attachments to entrap a target) to aid in their recruitment and intelligence gathering efforts. The KGB was notorious for using it's agents to entrap Western officials and personal using sexual blackmail or enticement in order to obtain information.
One example is that of John Vassal, a British official posted to the Naval Attache's office in the Moscow Embassy in 1952. Vassal was a homosexual, and as a result, was blackmailed by the Soviet's after they obtained compromising pictures of him with other men, to turn over information from the embassy and later the Admiralty's office in London itself. As far as other tactics (dead drops, number stations, disguises), they are accurate to a degree, though keep in mind, they are heavily used for dramatic effect at times, and aren't something I would point to as always being realistic depictions of their use.
One other thing to note, the show has had two plot points based on reality. The Toshiba-Kongsberg scandal (machine tools being illegally exported to the Soviet Union) and the beginnings of the "Star Wars" (Reagan's ICBM defense system) program have both made appearances so far. Though once again, being a show made to entertain, both of these have been heavily dramatized, and the reality of both of these incidents, is far more tame than the show has made them out to be. It's an entertaining show, but it's akin to watching a James Bond movie and expecting a movie based on reality.
If you're interested in learning more about the KGB's operational history during the height of the Cold War, two books I highly recommend for general readers are,
Spymaster : startling cold war revelations of a Soviet KGB Chief by TH Bagley
I believe one of the major influences on the show is the 2010 capture of 10 Russian spies operating as normal Americans in the US (dubbed the Illegals Program). The agents even had children together and raised families. In at least one case, the agents/parents confessed their true occupation and loyalty to their child, who swore to become a spy for Russia himself.