Interesting discussion of the greatest long tracking shots in cinema, starting with Touch of Evil but mostly limited to recent films.
There are really two types of long takes, and the above post is focused on the first type. That's a long tracking shot created for spectacular effect, usually taking in more than one room or location. In his description of a big shot from The Prisoner of Zenda (where the camera followed a character throughout a palace, past a ballroom full of waltzing couples, until he reached Niven and some other characters), David Niven called this a "production shot," because it shows off the lavishness and size of the production in a way that couldn't be accomplished with cutting.
There are other reasons to do this kind of shot besides just showing off, of course. Most of the examples cited in the post, as well as some of my own favorites (and my very favorite, Vincente Minnelli's "turning out the lights" scene in Meet Me in St. Louis, where the camera follows Judy Garland from room to room and adjusts in mid-shot to all the lighting changes), derive some of their emotional power from the fact that there's no cutting; the long take in Touch of Evil builds suspense because we instinctively know that when there's a cut, the bomb will explode. But it is a stunt shot, and it's designed to call attention to its difficulty. Like this take from Busby Berkeley's The Gang's All Here. He didn't have to do the whole second half of this number in one take, but that's part of the fun of this kind of long take: the director sets himself and his crew more difficulty than absolutely necessary.
I especially like Berkeley's gag of tracking past a bunch of women who sort of look like the film's star, Alice Faye, before finally giving us Faye herself at the end (anticipating by 25 years Jacques Tati's gag of the fake M. Hulots in Playtime).
The other kind of long take, which is much less ostentatious, is a dialogue scene shot all or nearly all in one take. This kind of scene is less expensive (because it doesn't require as much camera movement or as many sets), but requires a lot of rehearsal by the actors, who can't afford to miss a line or they'll have to start all over again. The longest take in Touch of Evil is like this: it involves Welles searching a room, and it doesn't announce itself the way the opening shot does (though he did have to use breakaway walls to move the camera between two rooms), but the actors all had to know their lines and hit their marks exactly.
This kind of shot is done less for show-offy purposes (since it's often not even noticeable that it's all in one take) than to get extra energy into the scene by having the characters truly interact with each other, instead of stitching the scene together from a bunch of different takes. It also had two side benefits: one, by doing a in one take, a director made it impossible for the producer to re-cut it. (That's one of the reasons why John Ford preferred to shoot with as little "coverage" -- additional angles -- as possible.) And two, if the actors were up to the task, this kind of shooting allowed the director to get a lot of script pages filmed relatively quickly. You may have heard the story that Orson Welles filmed that long dialogue scene in Touch of Evil on the first day of shooting, to convince the studio that he could get an entire scene finished in only one day.
This take from Sullivan's Travels is an example of the long dialogue take. Note that near the end of the take, the actor playing the studio boss almost flubs his line, but recovers ("Who's... t... talking about taking you off salary?").