DYNAMIC microphones do not require additional electricity to run.  They are durable and can tolerate high sound pressure levels.  Dynamic mics tend to have a full midrange but less clear high frequencies than other mics. Dynamic mics are handy for drums and other loud sounds, and some have a clear enough sound to work well for vocals and other delicate instruments. The SM57 is an important part of every microphone collection.

RIBBON microphones also do not require electricity, but the capsule is a fine metal ribbon rather than the sturdier components used in dynamic mics.  Certain ribbon mics provide the best sound for instruments such as horn and even voice. For my money nothing captures the spit of a horn better than an RCA 77 or 44. Unfortunately ribbon mics are more prone to overloading than dynamic mics, so be careful especially when you do not know how loud your musician will be. Like dynamic mics, ribbon mics do not need external power to work.

CONDENSER microphones use electrically charged capsules made of thin pieces of metal (such as gold).  They are more sensitive to high sound pressure levels but will more accurately capture all of the frequencies of the source sound, even the high frequencies. Condenser mics vary in warmth and air but in general are the best mics for capturing most sounds. Beware of using extremely bright condensers with some vocalists as the extra top can be a problem. My absolute favorite mics are the U67, U47 (and their cousins). I even use U87s on toms unless I think the drummer is so wild I need to use dynamic mics. The differences in sound means an opposite approach to processing the sound. The condensers give great attack (slap your outstretched palm sharply to hear the transient the condensers pick up well) and needed a little more meat. The dynamics had great meat but needed more attack. Yes some situations call for the dynamics over the condensers but for the most part give me my condensers.

All of these microphone types work in slightly different ways, and as a result sound different from each other. Depending on what it is you are trying to record, and whether you want to do so accurately or attempt to enhance it, one type might be more appropriate to use.

Knowing the sound of the different microphone types (and even models) will allow you to properly choose which mic to use for a particular purpose.  Often you will want flat, exact reproduction of what is being heard.  But frequently you will try to ENHANCE the sound of what is being heard WHILE you are capturing it.  And that means CHOOSING a mic that BEST MATCHES OR ENHANCES the sound of what is being heard.  Use a bright sounding microphone to record a bright sounding instrument, and a bassy sounding microphone for a low sounding instrument.

Of course, the MICROPHONE PRE-AMP that you are using to amplify the microphone will color the sound.  Take that into consideration when deciding what to use.  A clear condenser microphone through a meaty old Neve mic pre would be a very nice thing indeed.

Cardioid mics can capture very tight areas.  An AKG 414 set to hyper-cardioid is a great way to isolate the high-hat or snare bottom when tracking a drum kit.  A shotgun mic has a super-cardioid pattern.  Cardioid mics are very helpful when you are trying to mic only one sound source (or area) and avoid others, such as a live vocalist in front of a band (or one side of a stereo instrument).

Omnidirectional mics will record everything in the area.  All cardioid mics are really Omnis with phase cancellation.