It seems like a stupid question whose answer is just "it depends."
But truthfully there are a lot of thoughts that go into the decision of how many mics to use on something. There are some obvious ones and some less obvious. Let's take a look and break it down a bit. Some of these are reasons to mic, others are issues you will encounter.
1. Phase issues. - This seems to be the primary issue with using multiple mics. As you add more mics on a single source, the sound arrives to both mics at different times. The mics also have different characteristics that can lead to more phase issues between the two. Put up two mics on something and invariably you WILL have some sort of phasing, it's just a matter of how well it works for you. Sometimes the EQ differences you get from two different mics can be amazing when combined. Sometimes it's terrible.
2. Stereo width. - This is an obvious one. We use multiple mics to capture a stereo picture.
3. Ambience. - We may use a close mic and a room mic to get a direct signal and one less direct. This can be nice on just about any instrument and usually has a fairly nice phase coherency if you place the mics far enough apart. You can use the early reflections to your advantage.
4. Dual processing. - You may use two of the same mic but process them differently. One may go through THIS preamp with THAT EQ and with THAT compressor, etc.
5. Mix Options. - Also a very popular reason to use multiple mics. You may record a guitar cab or drumset with multiple mics, but only use a few come mix time. This is a fine reason, but sometimes can lead you into the habit of "safe mic'ing."
6. Safe Mic'ing. So what is this? This is a very common pitfall with lots of engineers out there. It is basically using a ton of mics to capture "all the parts of the sound" without actually taking the time to make each mic sound good. That type of engineering is a gamble - you put up 4 mics and hope one sounds good. That's bad news in my book. What you usually get is one that sounds okay and three that sound mediocre and are unusable with the first. There are phase problems, tonal incoherency, and the like.
7. Bright Mic, Dark Mic. - This is very common on lots of sources. A good example would be like an inside mic and an outside mic on a kick drum. One is for the bright attack of the beater, and the other is for the low thump. You also see it on guitar cabs - a 57 and a Ribbon combined can get a really great sound. The 57 is present and bright while the ribbon is dark and has a big low end. They compliment each other nicely.
8. Hifi Mic, Lofi Mic. - Also very common for vocals and drums. You'll have a condenser mic on a vocal to get the nice "pretty" vocal sound, but then another mic may be like a 57 or something running through an amp to get distortion. There are lots of applications of this. Guitar amps could even have like a 57 for a classic lofi sound and then a condenser for a hifi sound.
So with all of these considerations, how do you even start to pick? Here are some tips.
1. Figure out how big the source is in the song. If the source is an acoustic guitar and it's a solo instrument track, you will probably want a fairly large sounding acoustic guitar to take up a lot of space. If it's a vocal and an acoustic, it may need to be a bit smaller. If it's an acoustic with a band, it will need to be a lot smaller. The more tracks you have, the less space each can occupy. I'm talking stereo width wise AND frequency wise. Things will a big full low end may not fit in a dense track. You'd be better off recording it with a less bassy mic than trying to EQ it later. Or moving the mic backward to give it some more depth and also less low end.
2. Figure out what tonal role the source plays in the song. If the source plays by itself a lot, it may need to be bigger sounding. If it's in the track barely audible it doesn't need a super full frequency range.
3. Figure out how upfront the source needs to be, or it's spatial role. If something needs to be right upfront and in your face, mic it that way. Close. Under a foot usually. If something needs to sound farther away, mic it farther away. You should realize that not everything can be upfront and not everything can be far away. If everything is upfront, your mix will resemble a straight line of performers on stage with no front to rear depth.
4. Start with one mic. Always. On every Try to get the sound as good as possible with one mic and as close to the sound that you want with just one mic. This helps keep phase issues to a minimum and helps you focus. Then if you need to add more to a sound that you can't get by just one mic, then add another mic. Take a drumkit for example. You may start with one overhead. If you want more width, make it a stereo pair for overheads. If you need more kick (which you probably will), then maybe add an outside kick mic. Need more click? Add an inside kick mic. Need more snare? Add a snare mic on top. Need more floor tom? Need more room ambience? Add one by one. You get the picture. You may find that a drumkit sounds good and better with 4 or 5 mics than it would with 15 mics. It surely will sound more phase coherent, which will make it sound more solid and more well recorded.
5. Try listening for exactly what part of the tone you're missing. If you are recording an acoustic guitar with one mic and you feel like you need more midrange, try adding a dynamic mic someplace. Just because you add another mic doesn't mean you have to pan it. You can pan it straight underneath the other mic. To take the previous drumkit example, You likely will need more kick in your overheads just because OH mics generally don't contain a lot of kick. But, do you need more CLICK sound or more LOW END? It's likely low end. If you're recording electric guitar, try working with a handful of mics before you find the right one. If it's picking up everything really well but you just need a little more bottom end, consider adding another mic. Maybe just barely bring it up underneath.
6. Try Mid Side Mic'ing. Google it and learn about it. It's a phase coherent way to add depth and width to tracks like acoustic guitar and drums and room mics. It's a brilliant technique that works well in any genre.
7. The fewer mics you use, be less afraid of EQ. Obviously it would be best to get the sound right from the start, but if phase starts getting in the way, it'd probably best just to use a single mic with loads of EQ. It will sound much better to EQ a singular mic on a source rather than get phase between two mics. So, if you're doing drums with multiple mics, really try to get it as close as possible with the mics. Try not to EQ like crazy. The only thing you can really get away with EQ'ing crazy are the close mics, because they're so close. On a guitar, it may be best to use one mic and EQ it. Same with a vocal. It really does depend. When in doubt, use the BEST eq you can. That probably means analog EQ. Sorry plugins, I still have yet to find any plugin that really sounds quite like the hardware. My favorite plugin for EQ is DMG EQuality. That can really make me happy.
8. Sometimes I'll record an acoustic guitar with something like 4 mics. I know that sounds absolutely ridiculous, but I'll explain. I'll probably start with a mono SDC maybe 15" away at the neck joint. I like about that far away on acoustic guitar. I'll get that to sound as good as possible. If I need some more size and width, I'll throw up a figure 8 mic underneath for a Mid-Side setup. Then I may put up a room mic 6-10' back to get some ambience that I may or may not use. If I need a bit more midrange (sometimes acoustics can sound brittle and boomy, but not a lot of woodiness, which I really like on acoustic), I may add a mic down by the bridge, which has a characteristically midrangey tone. I may use a dynamic. I may use a condenser. How many of these mics will I use? Likely just one or two, but I may use different mics at different sections rather than having to EQ. For example, if the song starts with acoustic but then the band kicks in later, I will probably start with the SDC with the fig8 mic to get a big full sound. As the band comes in I may just use the mid mic. When the electric guitars kick in, I may just use the room mic to push the acoustic backward. And, if need be, I can try the midrangey mic to help it cut if it needs to. That's just an example.
I hope this has given you some things to think about! I've done some sessions with 15 mics on drums and others with 3 and been happy with both. Ive done some with ridiculous mic'ing setups for acoustic guitar for the purpose of picking a few in the mix later. Sometimes just one mic works. The more you engineer you will find good starting places of your own. Don't follow the books. Don't! Find your own starting places and build from there.
Inspired by my weird three mic vocal setup today:
Neumann KM184 > API Pre > Distressor
RE20 > Vintech X73 > Distressor > Tube Tech CL1B
SM57 (with a glass slide taped on to it) > Yamaha Mixer > Musket Fuzz Pedal > Reason Amp > 112 Cabinet > Fathead > Vintech X73 > Distressor > Dbx160.
