Many are like crime or police/detective novels in that the plot involves some misdeed planned or committed and the prevention or retribution thereof.
Novels of this genre often appeal primarily to the sense of righteous indignation on the part the reader. Those novels that have incomplete control of this aspect often tend to become tedious and objectionable recreations of the school-yard quarrels—he/they started this, he/they hit me/us first, and therefore whatever we did or do in retaliation is somehow justified. If that is not sufficient, then the writer might resort to more or less overt appeals to patriotism/jingoism. But then the “spy” part tends to get lost and the story could just as well be some more or less cunning version of cowboys and Indians. There is too much of this sort of writing that deserves to be lumped together as pulp fiction.
John LeCarre is deservedly celebrated for rescuing this genre from the spirited but otherwise not very edifying adventures of James Bond. His prose was brooding and sometimes precious—“Smiley had bored him; he looked sulky and cheated; distressing downward folds had formed on the lower contours of his cheeks….” Or, as Smiley drove past “the unlovable fascades of the Edgeware Road, the wind had dropped, the sky was black with waiting rain, and all that remained of the sun was a lingering redness on the tarmac.”
But he wrote also of the gritty aspects of spy-craft, of following and watching a suspect; how in certain countries “the security forces knew next to nothing about” its subtle requirements, “probably because no administration in living memory had to feel shy about it.” He wrote of the motivation for betrayal, a hope “to advance the Russian cause ahead of the American” but not to injure any British interest until the Suez incident “finally persuaded him of the inanity of the British position” and “he became a committed, full-time Soviet mole with no holds barred.”
More recently, David Ignatius (see for example, Bloodmoney: a novel of espionage) has written with insight into the enemies (or victims?) of the American war in Af-Pak, how some were created by the actions of the Americans as the Taliban and al-Qaeda are said to believe, how ingeniously the enemy had copied what the CIA had done to such great effect in “following the money” to track down perpetrators of evil against them, how they are bound by their own values of hospitality, vengeance and perhaps of sanctuary.
The "spying" usually lifts the genre beyond the boundaries of a particular country and gives the opportunity for the writer to explore cultural differences. Does this mean that some work like “The Tale of Two Cities” might be reclassified as a spy thriller? Probably not and in any case, the plot of that novel could very well have been framed for a purely English situation. Mayhem in foreign countries does not necessarily result in a spy thriller. Problems and solutions that cross national boundaries, the threat of violence and the need for secrecy in action—I believe these are essential. It will surely not hurt if the characters are interesting though spy thrillers do not need to be psychological (Smiley versus Karla) and should certainly not be paranormal.
At least these are my preferences; I have no desire to see them enshrined by any Academy or Official Body!