Large capsule condenser mics were once an element that defined a serious studio. They provide clarity and sparkle and give vocals a larger-than-life effect that is unmatched by any other mic style. Known as the "Swiss army knife" of the microphone cabinet, there are few applications that cannot employ this style of mic. The Neumann U-87 is the holy grail for many engineers, though most manufactures include large capsule styles in their product lines.
Also called "pencil" condensers, the small cap mic is an excellent choice for acoustic guitars and grand pianos. Its small size makes it convenient for stereo microphone arrays. All microphones exhibit a characteristic called off-axis coloration, in which frequency response changes when the source is not in front of the mic. Small capsule condensers are known for their reduction of this effect, making them ideal for use with distant mic techniques, like drum overheads.
Dynamic mics are by far the most common mic for live sound use. They are durable and generally more feedback-resistant than condenser mics, though at a cost of some sensitivity and fidelity. This doesn't mean they are not good studio mics. Shure's ubiquitous SM-57 is a standard mic for use on guitar amps and drums. Dedicated mics for bass drum are also common.
Ribbon microphones are technically dynamic mics, but unlike moving coil designs, ribbon mics are delicate and sensitive to blasts of air and rough handling. They have a special quality that keeps them in demand. Companies like Blue Microphone make unusual-looking mics with unusual frequency response. Special effects can be achieved with pretty much any mic you can connect to a recorder.