I’ve recently downloaded the following songs:
Secret Agent Man
Peter Gunn Theme
Get Smart Theme
I Spy Theme (the original show)
The Pink Panther Theme
The James Bond Theme (Dr. No)
Route 66
Okay, the last one really isn’t a ‘spy tune’ but it sort of fits the era and the ‘feel’.
What are some other spy tunes I can add to my playlist? I’ve thought of Mission Impossible and The Man From U.N.C.L.E. I don’t remember the latter, and my connection is too slow to sample it here.
Lalo Schifrin’s “Mission: Impossible” theme is a classic, and one of the rare pieces of popular music in 5/4 time. It’s definitely a worthwhile part of any music collection.
A lot of music from the band Portishead is inspired by spy movie soundtracks, and occasionally they even use samples. I think you would like them a lot. If you’re downloading songs, sample them with “Theme From ‘To Kill a Dead Man’” and “Sour Times (Nobody Loves Me).”
Also, because of the reverb-drenched twangy guitars played in minor keys, there is a lot of crossover between surf music and spy movie music. Check out bands like the Aqua Velvets, the Volcanos, Spies Who Surf, Man… Or Astroman?, and Los Straitjackets for a lot of spy/surf hybrid sounds.
Yeah, that’s probably going to be downloaded next time.
I like Portishead, but I was hoping to stick to ‘classic’ tunes. That is, tunes that were made during the era.
I have a separate Beach Music playlist with classic surf bands, plus The Big Kahuna And The Copa Cats and The Mermen. 
“Contact in Red Square” - Blondie (from their underrated Plastic Letters album).
Not sure if this violates your “classics” criterion, but the various Bond movies have “opening credits” songs besides the Bond theme proper. A recent one that I’m especially a fan of is Garbage’s “The World Is Not Enough.”
Definitely the Avengers TV theme. And while you’re at it, maybe the Prisoner and Perry Mason themes. (The latter has nothing to do with spies, but I think the music would fit in nicely on your list.)
Best Bond song, worst Bond movie. 
(Well, not really. Best Bond song is “Live and Let Die” and the worst Bond movie is “You Only Live Twice” (that’s the crappy re-make of Thunderball done by a different studio, yes? But “The World is Not Enough” has the higest good song to crappy movie ratio.)
I have to agree with that. In fact, the video of the title song that was on the The World Is Not Enough DVD was better than the movie itself.
Um, no. Best Bond theme: the instrumental to On Her Majesty’s Secret Service; the worst film is a tossup (or would that be upchuck?) between The Man With the Golden Gun and Moonraker, and the crappy Thunderball remake was the non-canonical Never Say Never Again.
The theme from Hawaii 5 o?
That lets you leave out the Xmas tree song, right?
Sneaky.
Unless you’re like me and have a huge crime jazz soundtrack collection that you’ve spent years on, you’d probably be content with just the songs from the Crime Jazz: Music in the First Degree and Second Degree and Ultra-Lounge: Crime Scene compilations. Google those as well as “crime jazz” and you should be set for weeks.
No love for “The Saint”? (I actually prefer Graeme Revell’s version of The Saint Theme from the 1997 film, which is the only way in which that film could be considered remotely superior to the show.)
They’re not exactly spy shows, but the title characters are ex-spies: “Stringray” (with the title theme by Mike Post and Pete Carpenter), and The Equalizer (which I believe was composed by Stewart Copeland).
The film was awful, but John Barry’s score for Moonraker (with the title track sung by three time Bond vocalist Shirley Bassey) was haunting. He did similiarly good work on The Living Daylights (though I thought he should have worked a zither in there somehow, just to reinforce the homage). It’s a toss-up as to whether the brassy Goldfinger score or the experiemental orchestral fusion tracks for On Her Majesty’s Secret Service are his best work. The Barry-esque theme music to The Incredibles is also worth note.
Stranger
The Bagman’s Gambit, by The Decemberists. Awesome song.
Opening verse:
*
On the lam from the law
On the steps of the capitol
You shot a plainclothes cop on the ten o’clock
And I saw momentarily
They flashed a photograph, it couldn’t be you
You’d been abused so horribly
But you were there in some anonymous room
And I recall that fall
I was working for the government
And in a bathroom stall off the National Mall
How we kissed so sweetly
How could I refuse a favor or two
For a tryst in the greenery
I gave you documents and microfilm, too
*
How about Weird Al’s Spy Hard?
Whenever I feel the need to be a secret agent, I tend to listen to Secret Agent (The soundtrack for your stylish, mysterious, dangerous life). It’s an internet radio station, put out by SomaFM (The link creator button doesn’t seem to be working for me right now and I can’t remember UBB code, but their URL is www.somafm.com)
All the music on it sounds like it belongs in a spy movie, and the songs are separated by clips from various Bond movies. It’s great.
The Johnny Rivers Secret Agent Man (direct link to mp3) theme was used for the later seasons (known in the US as Secret Agent) of the series that started out in the UK as Danger Man. Here is a page with MP3 downloads of the various seasons of Danger Man; the one most familiar to UK listeners is probably the second one on this page, by the Edwin Astley Orchestra.
I’ll second Biffy’s recommendation of The Prisoner, and add the theme (wav file) to The Sandbaggers.
No, no, people. The worst Bond theme has to be that wretched piece of technocrap by Mrs. Guy Ritchie, “Die Another Day.”
I don’t suppose Spy In The House Of Love is at all what you’re looking for?
(I didn’t suppose. But I’ve been listening to the dB’s today.)
There’s a compilation called The Avengers and other Top Sixties TV Themes that’s not stellar, but not bad either. It’s got “The Avengers,” of course, as well as “The Saint,” a bunch of Gerry Anderson series, and some stuff I’ve never heard of – mostly British TV.