Suspension is the part of an automobile (or other wheeled vehicle) which absorbs shock from the road (or other driving surface) by traveling vertically. This is generally performed using a system of lever arms and springs. Various types of auto suspension have various drawbacks and advantages. The original system of a sprung suspension, consisting of a fixed axle mounted on leaf springs, first used in horse-drawn carriages and wagons, is still in use today.
Basics
As a vehicle travels forward, it encounters variations in the road. Inertia causes the vehicle to want to continue heading as it has been heading, but the road's surface disagrees. The resulting force, applied to the tires, is translated into upward motion of the suspension. This upward motion is used to compress a spring, storing the energy, and pushing the suspension back down, or pushing the car up. The motion is both damped and limited by a shock absorber, or shock. These devices limit the maximum rate of compression, or closing of the suspension, and rebound, or opening. Without them, vehicles are sluggish during cornering and bounce around or lurch and roll over bumps and through dips.
Some of the more important characteristics of a suspension include travel, or the maximum vertical range of motion; compressing force, or spring rate, shown in foot-pounds or kg/mm; damping, provided by shock absorbers; camber, or the angle at which the wheel meets the ground, leaning sideways; caster, the angle at which the direction of suspension travel meets the ground, fronty to back; and toe, the angle at which a wheel points left or right. Of immense interest is deflection, or the degree of camber or toe change during suspension travel.
Automobiles
On various cars, only subsets of the suspension characteristics are typically adjustable. In particular, changing front camber and toe and rear camber only is what typically makes up an automotive alignment job, though all of those things affect handling. Camber is one of the most important, because during cornering, where handling matters the most, it can cancel or mitigate the effects of body roll. Finally, the unsprung mass or unsprung weight, the amount of mass which must travel up and down with the wheel. This gives the suspension member inertia which affects the rate at which it recovers from compression.
Fixed or Independent?
A suspension in which both wheels on an axle (IE, typically either front or rear) are independent of one another, is known as an independent suspension. If a fixed axle is used at all, it is most common for the front suspension to be independent and the rear to be a fixed axle, in which there is a literal solid axle between the wheels. This is the typical form for two wheel drive trucks, and just about every American car until the 1980s. However, especially in front wheel drive cars, there has been a drive towards independent rear suspension, or IRS, as it provides superior handling. This is actually cheaper and saves space in front wheel drive cars. It is desirable on all vehicles, however, for its superior handling characteristics.
Independent suspensions generally cost more to produce, but they are functionally better. There are a variety of independent suspension designs out there; The most common are the MacPherson strut suspension, double wishbone, multilink, and torsion beam designs. Double wishbone and multilink are arguably the best, and are used for the vast majority of sports and racing cars. A few cars (F1 and CART types sometimes use a bellcrank suspension in which the shocks are mounted horizontally to save vertical space, for aerodynamics reasons. There are also trailing arm, semi-trailing arm, and Weissach axle designs.
In general, independent suspension allows greater travel and improved handling, but fixed-axle type suspensions are cheaper and stronger. The greatest benefits of independent suspension are improved handling off-road and when the camber of the road changes. Fixed axle vehicles perform well in flat-road or -track scenarios and with hard suspension and sway bars to minimize body roll. However, they do not do particularly well anywhere else.
Springs
As far as the springs in suspension, they are generally one of two types; coil, or leaf. Leaf springs are several leaves of flexible metal; The further the vehicle is pressed down (or the suspension is pressed up) the more pieces of metal are bent (in some designs) or the further the bundle is bent; Either way, the resistance rises. You can get bolt-on spring limiters and helper springs to enhance leaf springs. Coil springs can be mounted around a shock or strut, or next to it. Furthermore, they can come as a single or progressive rate spring. Progressive rate springs have multiple rates twisted into them, and so will absorb short bounces without transmitting much force to the chassis. Some suspension systems use charged gas shocks, which actually support some of the load of the vehicle, but in general the entire weight of the vehicle rests upon the springs and the shock absorbers do nothing but damping.*
In fact, not all suspensions depend on springs to support the load. The 1957 Cadillac Eldorado Brougham utilized a compressor-driven air shock system using rubber diaphragms, and Citroen has famously produced air-operated suspension as well. This is the norm in bicycle suspension (see below) due to significant weight savings over a steel coil spring.
There are also active suspension systems. These use some sort of sensors and actuators to actively change some aspect of the suspension, whether it be ride height or damping levels. This is actually used for several purposes. Jeep developed a system that allowed one of their vehicles to literally drive over a foot-tall obstacle. Generally speaking, the sensors used for this type of active suspension are optical and use infrared light, though both sonar and radar can be used (and have been, in prototypes.) The actuators are typically hydraulic. The most common and inexpensive active suspension system is the air bag, heavy-duty examples of which are commonly installed in the rear of semi-tractor trucks. These compressor-driven systems resemble nothing more than a heavy-duty balloon, although they are sometimes enclosed in a canister for protection.
Another hydraulically-driven active suspension system is the Mercedes automatically leveling suspension. Found even on older vehicles (beginning in the seventies) this system uses a hydraulic valve connected to a lever on the rear sway bar to detect and compensate for excessive squat. As the suspension compresses, the sway bar rotates, thus the linkage moves and changes the valve position. A hydraulic pump attached to the engine runs to the valve in the back, which in turn runs to the rear suspension.
Finally, there is a third type of active suspension which lowers the vehicle at higher speeds in order to improve handling. The vehicle rises back up when you are going slower, in order to deal with speed bumps, curbs, and other road hazards.
Motorcycles
Motorcycles (two-wheeled vehicles) also feature suspension to enable them to track the road. Typically motorcycles have a rear wheel somewhat tightly integrated to the frame (attached with a single or double swing arm or in older models, not suspended at all) while the front wheel rests at the end of a fork with integrated springs and dampers. Motorcycles differ from cars in that they are tilted to steer, so the suspension forces are substantially different. Instead of the bearing on the wheel receiving a substantial sideways load, the tire must handle most of the force of cornering. Since they do not have two sides, motorcycles have neutral camber. However, the caster angle is of paramount importance, and controls the centering of the front wheel, which in turn leads the motorcycle to want to travel upright.
Most motorcycles have less than six inches of suspension travel front or rear, but dirt bikes and enduro motorcycles may have a foot or more in the front, and perhaps eight inches in the rear. The rear suspension of the motorcycle usually is sprung and damped with a coil-over unit between one or more rear swing arms and the upper rear frame, but variations have placed this shock in nearly every imaginable location, including horizontally under the seat, or even horizontally underneath the entire frame. Each approach has its own advantages, although it's hard to imagine a worse place for a component which can be damaged by rock impact than directly beneath the vehicle.
Bicycles
Since about the 1970s, bicycles have been produced which feature moving suspension parts. The earliest examples are undamped and use only a spring, which produces a bouncy ride. Still, it helps to absorb impacts. While some examples of even these early suspension bicycles have rear suspension, after these bicycles faded out and were replaced with "BMX" bicycles designed to be ridden over obstacles while standing, bicycle suspension first returned to the mass market in the form of front suspension on mountain bikes. Front-only suspension bikes are known as hardtails while full-suspension bikes are called softtails.
The front suspension of most modern bicycles is substantially similar to that of a motorcycle, differing only in scale. The longest-travel bicycle fork in production will compress about twelve inches, putting it well into motorcycle territory. Most forks only compress four inches at the outside, but some of your basic longer-travel examples have over six inches of motion. Most rear suspensions utilize a triangular arrangement which looks like it was lifted off of a typical hardtail bicycle, and whose shock travels forward to the lower tube, but there are notable examples including the ca. 2000 K2 Evo, which utilizes a motorcycle-style double rear swingarm.
* "Shock absorber" is actually a significant misnomer. The springs actually absorb the shock, although some of it is converted to heat when the medium inside the shock absorber (oil or gas) is forced through the narrow apertures that cause it to work. The shock absorbers are actually dampers (like a dash pot) in that they primarily limit the maximum rate of travel. Thus, they cause more shock to be transmitted through the suspension in exchange for preventing your car from constantly rocking and bouncing uncontrollably due to traveling over bumps.
References:
Website: Autozine Technical School (http://www.fortunecity.com/silverstone/lancia/58/technical_school/tech_index.htm)