Guitars are inordinately popular in popular music, usually come in three guises; acoustic, electric and bass. Electric and Bass are likely to have their own 'combo' amplifier, which you then mic up, rather than taking a signal straight from the instrument to a DI bow (although this happens often with bass).


Use the best mic you can, preferably capacitor, for the sensitivity and response; because of the 'artists' hands, the mic can only be directed at the sounding hole/mid-body area. 
To get a natural sound, informatin must be collected from a larger area of the guitar, but this will pose porblems in a live environment, so usually, a short distance (up to 2 feet) from the sounding-hole is used. Often the output of this mic is combined with signals from a pickup, giving ambiance and detail.
Pickups suffer from feedback, because the entire body (sound box) of the guitar vibrates with the PA, which vibrates the strings that feed the pickup ie: feedback.
This is why when acoustics feedback it's a 'midrange' sound (the box resonance) rather than the 'squeal' that mic's produce. EQ's can eliminate just this frequency, but obviously, will effect the tonality of the guitar.

Generally, EQ acoustics as little as possible; like singers, the instrument makes the sound, you're just 'relaying' it. If needed, cut below 200Hz to bring the sound out a little.
To sound all 'country', steely-stringed, boost 4-6kHz, y'all.


Position mic right up against grille (not touching). Sound alters significantly depending on where the mic is relative to the cone of the guitar amp. Generally the more directly towards the centre of the dustcap, the brighter the sound will be. Obviously, the further out, the mellower the sound will get. Half-way is a good all round, allowing desk EQ to shape the final sound if needed. 
Consideration may be taken into open-backed cabs, where lots of sound does escape from the back of the cab. A more-distant mic may benifit if you want to obtain the complete sound, or mic'ing the back of the cab will give a phatter overall sound.

Beware of physical pickup from the mic stand (esp. on bass amps) as it's now very close to the heavy guitar amp. Not so much for feedback (as amp isn't fed off mic) but for musicality. Choice of mic is quite unimportant, as guitar cabs themselves have inherently limited response.

Warm the sound at 125-200Hz; cut below the lowest possible note (82Hz) to improve clarity and reduce the obvious hum that occurs with guitar pickups (esp. mains hum). 2-4kHz increases attack.... remember that backline rarely outputs above 5kHz, so unless DI'ing the guitar, get rid o it. Electric guitar has no 'correct' sound, so experiment with the EQ more than normal to see what you can 'create'. 


Often DI'd as 'cleaner' bass sound is normally desired. If a Bass Amp is mic'd, position mic a few inches from the front grill, rather than right against it. Choose mic carefully (if you can) to get a suitable dynamic response. Remember compression and chorus work well on Bass.

When engineering, although the lowest guitar note is 41Hz, 80Hz pushes out the lowest notes well, whereas boosting 500-800Hz creates an aggressive, rocky, noise. Anything higher picks up finger and handling noise, but little else. Conversely, cutting at about 250Hz can 'warm' the sound without getting too upfront.
To improve the general presence, boost 2.5-5kHz slightly (as with kick drums).