Microphones have different pickup patterns, or directional capabilities. This page briefly discusses the more usual patterns used in video production, there's quite a few other types. Depending on the type of work that you're doing, some microphones are more suitable than others, and some will be completely unsuitable.
Omni-directional microphones pick up sounds coming from any direction with equal sensitivity. You might use an omni-directional microphone when recording group activities, and you want to pick up everything without moving the microphone around. Or, you might want to be able to move the microphone around without noticing the accoustics changing radically. Omni mikes usually have a very good frequency response, they're typically much wider and cleaner than other types, and the response isn't affected by proximity.
Uni-directional microphones are mostly sensistive to sound coming from in front of them. And super-directional microphones are even more so. You'd use directional microphones when you need to concentrate on sounds coming from a specific direction, especially when you can't get close enough to the source. Uni mikes typically emphasise the bass of anything that's really close to the microphone, and the converse for anything far away (distant sounds will lacking in bass and clarity).
Noise-cancelling microphones actually cancel out ambient noise to only reproduce what's directly aimed into them at close range. Noise-cancelling microphones are usually used for special purposes, such as recording someone in the middle of a noisy environment, or for intercom systems in a noisy place, where you want to hear only the sound of the one person speaking directly into the microphone. Most will only pick up sounds that are really close to the mike (around about only an inch away from their lips), and good ones will cancel out almost all ambient sound.
When miking large places, such as a group of people in a room, or a stage play, you've got a few ways of doing that. You can use one omni mike to get the whole lot in one go, but you might have to play around with placement so that it's nearest to your sound source and further from the audience, or vice versa, depending on the ambience you want, and the relative loudness of each. Similarly, you can use a pair of mikes to make a stereo recording. You can place several omni or uni mikes in strategic places to pick up different things, and mix them together. You can individually mike everything. And you can do combinations of some of the above.
It's hard to say that one scheme's better than another, though a single mike can be the worst. You might find you're riding mixer levels up and down all the time, as some things are wildly different in levels. At least with a multiple mike set-up you can set levels for performers and crowd more individually, for instance, and not have to keep changing the sound level of your performance trying to cope with shrieking crowds clipping the sound levels.