What I find ingenious about Mission: Impossible (the first season finally came out on DVD today) is that creator Bruce Geller figured out how to provide a TV equivalent for a genre that normally doesn't adapt well to TV: the caper story.
Caper movies were all the rage in the '60s, but as we've seen this past season (with the almost instantly-canceled Smith), capers don't usually work in a television series format, because audiences don't usually come back to root for the criminals week in and week out. A movie like Rififi or Topkapi or even The Lavender Hill Mob only expects us to follow the criminals until this one job is done. But you can't ask people to cheer for the crooks week after week, not until The Sopranos anyway.
So what Geller did in Mission: Impossible was to take all the familiar devices of the crime caper -- the elaborate plan, the team members with different specialties, the suspenseful twist when it looks like the plan has gone wrong -- and create a format where the devious team was, if not on the side of the law, at least on the side of goodness and decency. But there was still that element of outlaw-ishness, because these characters weren't officially sanctioned; the American government hired them secretly, promising to disavow any knowledge of their actions, and they violated international law just about every week. So although the members of the Impossible Mission Force were more sympathetic than the purely selfish characters in most caper films, they weren't squeaky-clean either; unlike, say, the guys in The Guns of Navarone, their plans had an air of rebelliousness about them because they weren't playing by normal rules or working for anyone recognizable as an authority figure (except that mysterious voice on the self-destructing messages).
Here's the opening scene from the pilot (where Wally Cox was the guest star as a safe-cracker; remember that many of the episodes, especially early ones, would have an additional member who wasn't part of the regular team). You'll notice that this was one of the few prime-time filmed shows of its time that made occasional use of a hand-held camera; in this case we see a hand-held shot when the team is introduced playing cards.