Inside the Capacitor
A capacitor consists of terminals that connect to two metal plates separated by a non-conducting substance, or dielectric.  In theory, the dielectric can be any non-conductive substance. However, for practical applications, specific materials are used that best suit the capacitor's function. Mica, ceramic, cellulose, porcelain, Mylar, Teflon and even air are some of the non-conductive materials used. The amount of charge that can be stored depends on the surface area of the electrodes, the strength and composition of the insulation between them, and how close they are together.  The dielectric dictates what kind of capacitor it is and for what it is best suited. Depending on the size and type of dielectric, some capacitors are better for high frequency uses, while some are better for high voltage applications. A capacitor's storage potential, or capacitance, is measured in units called farads. A 1-farad capacitor can store one coulomb of charge at 1 volt. A coulomb is 6.25e18 (6.25 * 10^18, or 6.25 billion billion) electrons. One amp represents a rate of electron flow of 1 coulomb of electrons per second, so a 1-farad capacitor can hold 1 amp-second of electrons at 1 volt.  Larger commercial supercapacitors, also known as ultracapacitors, have capacities as high as 3,000 farads.

Capacitor Types

Ceramic
Ceramic capacitors are normally used for radio frequency and some audio applications. These capacitors range in value from figures as low as a few picofarads to around 0.1 microfarads. In view of their wide range and suitability for RF applications they are used for coupling and decoupling applications in particular. They are by far the most commonly used type being cheap and reliable and their loss factor is particularly low; although this is dependent on the exact dielectric in use. Their stability and tolerance is not nearly as good as silver mica types, but their cost is much less.

There are a number of dielectrics that can be used. For low values a dielectric designated "COG" is normally used. This has the lowest dielectric constant but gives the highest stability and lowest loss. Where higher values are required in a given size, a dielectric with a higher dielectric constant must be used. Types with designations X7R and for higher values, Z5U are used, however their stability and loss are not as good as the capacitors made with COG dielectric.

Plastic film capacitors
The most common types of plastic film capacitors include polycarbonate, polyester, Mylar, and polystyrene. Each has its own properties, allowing them to be used in specific applications. Their values may range anywhere from several picofarads to a few microfarads dependent upon the actual type. Normally they are non-polar. In general, they are good general-purpose capacitors that may be used for a variety of applications, although their high frequency performance is not usually as good as that of the ceramic types.

Electrolytic
This type of capacitor is the most popular type for values greater than about 1 microfarad. It is constructed using a thin film of oxide on an aluminum foil. An electrolyte is used to make contact with the other plate. The two plates are wound around on one another and then placed into a can that is often aluminum.

These capacitors are polarized, and care should be taken to ensure they are placed in circuit the correct way round. If they are connected incorrectly they can be damaged, and in some extreme instances they can explode. Care should also be taken not to exceed the rated working voltage. Normally they should be operated well below this value. Also in power supply applications significant amounts of current may be drawn from them. Accordingly, capacitors intended for these applications have a ripple current rating which should also not be exceeded. If it is, then the component may become excessively hot and fail. It is also worth noting that these components have a limited life. It is often as little as 1000 hours at the maximum rating. This may be considerably extended if the component is run well below its maximum rating.

These capacitors have a wide tolerance. Typically the value of the component may be stated with a tolerance of -50% +100%. Despite this they are widely used in audio applications as coupling capacitors, and in smoothing applications for power supplies.

These are normally contained in a tubular aluminum can, each end being marked to show its polarity.

Tantalum
Ordinary aluminum electrolytic capacitors are rather large for many uses. In applications where size is of importance tantalum capacitors may be used. These are much smaller than the aluminum electrolytic and instead of using a film of oxide on aluminum they us a film of oxide on tantalum. They do not normally have high working voltages, 35V is normally the maximum, and some even have values of only a volt or so.

Like electrolytic capacitors, tantalums are also polarized and they are very intolerant of being reverse biased, often exploding when placed under stress. However their small size makes them very attractive for many applications.

Ultracapacitors
Ultracapacitors, also known as supercapacitors or electrochemical double layer capacitors (EDLC), are electrochemical capacitors that have an unusually high energy density when compared to common capacitors, typically on the order of thousands of times greater than a high-capacity electrolytic capacitor.  They are mostly used for power smoothing, but also for motor start in large diesel and submarine engines.

Researchers John Kassakian and Riccardo Signorelli at MIT replaced the activated carbon in ultracapacitors with a dense, microscopic forest of carbon nanotubes that is grown directly on the surface of the current collector.  The idea is to produce a larger surface area for electrons to collect and hence improve storage density. This improved storage coupled with fast charge times could allow capacitors to replace fuel cells in electric cars.

Sources:
http://spectrum.ieee.org/nov07/5636
http://en.wikipedia.org/wiki/EEstor
http://www.electronics-radio.com/..../capacitor-uses.php
electronics.howstuffworks.com/capacitor.htm
http://www.economist.com/science/displaystory.cfm?story_id=10601407
http://www.radio-electronics.com/info/data/capacitor/capacitor_types.php