In the following article I will give you a good idea of how to mic various popular instruments, as well as recommended mics for the job. These tips apply to both live and studio sound. Remember, nothing is set in stone and these should be used as general guidelines and starting points, rather than the way things must be done. Many a good recording has been done using different mics and techniques from those mentioned.

Snare Drum (Shure SM57, AKG C414, Sennheiser 421)
For the snare drum, it's always a safe choice to use a Shure SM57. Bring it in from the front side of the kit (pointing towards the drummer) and give it a 45 to 60 degree angle with the capsule about an inch or two above the head. The farther away it is from the head, the more room sound you will get, but the more chance of getting phase problems with other mics. The closer to the head you get, the more bottom end you'll get. For really deep snare drums, I sometimes find it neccessary to add a second mic below the drum to capture the snare sound. Just be careful of phasing problems again.

Toms  (Shure SM57, Shure Beta57, AKG C414, Sennheiser 421)
Mic all three toms with the mics set at a +/-45 degree angle to the drum head with the capsule pointing at an imaginary spot about 2" past the rim nearest you as you place the mic (this is assuming you're working from the audience side of the kit). The floor tom mic can be placed a little closer to the center of the head, but not too close. The distance of the mic from the actual head should range between one inch and six inches depending on how "roomy" you like your drums to sound. The further the mics are from the drums, the roomier the sound, but you'll have to pay more attention to possible phase cancellation problems.

Kick drum (AKG D-112, Shure Beta52, Sennheiser 421) If the mic you're using has a pad switch, use it. If not, pad the input at the mixing desk. Mic the kick drum from the audience side, but only after throwing a sandbag in the drum to weigh it down. Let the sandbag touch the head (that the beater hits) just enough to dampen out any obnoxious overtones, but not the good, natural sounding ones. The mic should be placed about half way in to the drum itself and pointing at the beater. If you bring the mic in from the right side of the drum and angle it at the beater you will be avoiding leakage from the snare drum, which is a good thing to do. You can experiment with the depth of the mic, but always keep the mic pointed at the beater for maximum attack. If you want a roomier sound, you can pull the mic out of the drum a little bit.

Bass Guitar (DI Box, AKG D-112, Shure Beta52, Sennheiser 421)
Using a direct box is the most common way to record or amplify a bass. Coming out of the direct box into the mixing desk's preamp or an outboard preamp will give you the ability to get the appropriate amount of gain. When using a mic on a bass cabinet, place it a foot or two back from the amp, as bass notes have long waveform, and require some air to fully develop. The closer your mic is to the amp, the more attack and edge you will hear. Farther away will give you more bottom end.

Cymbals (Rode NT4, Rode NT5, Oktava MC012, Shure SM81)
Using overheads can be very simple or very difficult. The important thing is to watch out for phase cancellation. The overhead mics will often interact with other drum mics, causing phase problems as dropouts at certain frequencies in any or all of the drums. Start with the two mics about 40cm over the cymbals, and point them straight down, looking directly at the center of the cymbals to achieve a more bell-like sound. Another option is to angle the mics toward the outer edges of the cymbals to get a brighter sound. The closer the mics are to the cymbals the less chance you will have of experiencing phase problems. If you do experience phase problems, it's often fixable by simply flicking the phase switch on one of the mic inputs or the other. A good rule of thumb is to always make sure that the distance between the two mics is at least twice as far as the distance between each mic and the cymbal it's over. To get a roomier or bigger drum sound, just raise the mics higher.

Hi-Hat (Shure SM57, Sennheiser 421, Shure SM81)
You may find that you don't need a separate mic on the hi-hat because there is enough of it leaking in to the other drum mics. If you do need to mic a hi-hat it's a good idea to place the mic about an inch away from the outer edge of the hi-hat. It's also a good practice to angle the mic away from the kit so that the hi-hat mic doesn't "hear" too much of the snare or other drums. Because you don't want any extraneous low-end rumble from the rest of the drum kit, it's recommended that you use the mic's roll-off switch if it has one, or use the mixing desk's high-pass filter or equalizer to eliminate low-end information from cluttering up your hi-hat signal.

Acoustic Guitar (Pickup, Rode NT5, AKG C3000, AKG C1000, Oktava MC012)
Acoustic guitar is difficult to get a great sound from. While not ideal, pickups are the best bet for stage work as they give a decent representation of the guitar and have the added benefits of being feedback resistant and allow the guitarist to move freely. For studio, micing is best. A condenser mic will almost always sound better than a dynamic mic. Get down on your knees and position your ear as if it were the microphone while the guitarist is playing. Move your ear around to find where it sounds best and place the mic there. If you have somebody assisting you, have them move the mic around what you think will be the sweet spot while the player is playing.

Electric guitar (Shure SM57, Sennheiser MD421)
The most important factor in getting great electric guitar sounds is that the sound coming out of the amp should be great. That's determined by the guitar, the amp, and the person playing it. With a multi speaker amp, you will often find that one speaker is "sweeter" sounding than the other(s) - mic this one. Many guitarists will be able to tell you which is the best speaker. Set up the mic right against the amp's grill, pointing it directly into the speaker or at a slight angle from the outer rim of the speaker pointing toward the middle. In studio you may want to use a second, ambient room mic a metre or more back from the amp. Usually a condenser.

Piano (Rode NT5, AKG C414, AKG C1000, AKG C3000)
Condenser mics are preferred. Pianos are usually miked and recorded in stereo, but don't necessarily have to be. The best starting point is to place one microphone over the bass strings at a height of 10-15cm, and the other mic over the upper register strings at a matching height. It's important to keep the mics on the same plane to avoid phase cancellation problems. It's also important to keep the mics separated by a distance of a couple of feet to help in avoiding phase problems. You will find that placing the mics closer to the strings gives you a sound with more attack, while raising the mics up will give a richer, fuller sound with less attack. If you are looking to get a sound with lots of percussiveness, place both mics nearer the hammers in order to get the sound of the hammers hitting the strings. If you are micing a solo piano or recording, keep the piano lid open to get a more natural sound. However, for live, close the lid most of the way to avoid leakage.

Synthesizer/Electric Piano (Direct)
This is an easy one! Don't use a mic. Plug it straight into your mixing desk, make sure nothing distorts and that's it!

Vocal (Live: Shure SM58, Shure Beta58. Studio: Rode NTK, AKG C3000, AKG C1000)
Personal choice is very much a deciding factor for mic choice.  Most engineers will use a large-diaphragm condenser mic to record vocals, and dynamic mics for live. It's hard to go wrong with a Shure Beta 58 for live. A pop filter for recording and a windscreen live is generally a good idea.

Percussion Instruments (Shure SM 57, Sennheiser MD 421)
For congas, timbales,etc. place the mic about eight inches above the drums, and angle them from the center of the drum looking out toward the sides. Shakers, tambourines - roll off the bottom end at the desk. Live, a vocal mic will always do - don't set up two mics for a vocalist who plays percussion.