The most realistic of all spy films and television is Danger Man, staring the television genius that was Patrick McGoohan. The first series ran from 1960-62, predating all other major spy series, however it's not very good, since it had a limited budget and tried to fit an hour long show into the half-hour format, although it was popular.
The second series had a bigger budget and ran from 1964-68 was and still is popular throughout the world. The Americans ran it as Secret Agent and gave it a rather annoying theme song. It's a great edge of your seat type of adventure series that is often humourous too.
I find John Drake to be the most believable of all spies. He plays the character as sort of a civil servant working for British Intelligence, which I suppose is what all spies really are and he takes his job very seriously. Drake is sent to deal with problems that can't be solved with traditional diplomacy. He is required to infiltrate and gain the trust of those involved in the messy situations so that he can alter the outcome in accordance to his orders. Most of the time he has to prevent traitors from handing over their secrets, rescue kidnapped scientists and VIPs, investigate crime rings, track down missing documents, prevent military coups in Africa and South America and prevent important people from defecting. To do this, he would adopt a character suitable to infiltrate the situation, usually a journalist, bland diplomat, brainless playboy, bumbling tourist and once even a butler.
What makes the show realistic are that the situations that Drake finds himself in are believable and there is not always a happy ending.
Drake is also infallible, he does make mistakes, gets arrested, allies betray him and equipment and plans fail. He also occasionally clashes with his superiors, who sometimes lie to him. However, Drake is also a moral man as he is rarely armed and uses his intelligence, charm, humour and quick-thinking to solve problems rather then killing everyone. He is also never romantically involved and has few friends, because the nature of his job makes it hard to form lasting relationships and to completely trust anyone. McGoohan also wanted to make a family-friendly show, although there is usually just one fist fight an episode.
The gadgets used were often bought off the self and were continuously re-used, particularly a camera hidden inside a cigarette lighter and a tape recorder hidden inside an electric razor. The costumes too came from off the rack and were rarely over the top, which makes for a fantastic study everyday fashions of the Sixties. And wait till you see the different types of men's hats that Drake wears!
There are 47 episodes of the second series of Danger Man and my favourite episodes are: "You're Not in Any Trouble, Are You?", "A Date With Doris" and "Don't Nail Him Yet"
Here's a video trailer from the 90's
Here's a clip from an episode
N.B. John Drake is not Number Six.