Multiple takes generally happen because the director wants multiple interpretations of the scene, so he can go back later in the editing room and have a number of options available to choose from for the final product. As an example, I was recently listening to the director’s commentary for an ep of “Six Feet Under” for a scene where Ruth has a break-down outside of the knitting shop. The commentary explained that they did a bunch of takes to cover the entire spectrum of intensity, everything from full-on sobbing to just a quiet teary moment. They ended up going with something in the middle.
Also because sometimes things just go wrong, especially if you’re on location (hi I’m saying my line and a car drives by and honks in the middle), or you’re working with small children or animals (try making a cat walk across the room on command. Go ahead, I dare you. ).
As already noted, sit-coms and other “recorded live” shows have three cameras running simultaneously, and usually only one take. For dramas, they might actually have multiple cameras available, but the logistics of the set-ups require multiple takes. If you’re filming a conversation between two people, a standard technique is the “over, over, two-shot” which is basically – one angle over Guy 1’s shoulder, looking at Guy 2’s face; one angle over Guy 2’s shoulder, looking at Guy 1’s face; one wide shot showing both of them. For any of these set-ups, if you tried to use more than one camera per take, the cameras would be visible to each other in the shot. (This is called “coverage” btw – multiple takes to capture multiple camera angles and shots.)
There are VERY few scenes in movies or TV dramas that are filmed in one take, or where the different camera angles for a single scene all came from the same take. Except for things like oners (one long shot where the camera follows the actor [or the action] around), it’s logistically impossible. Hell, sometimes one side of the coverage isn’t even filmed the same day as the other, and two actors may be having a conversation “with each other” that’s actually weeks apart.