There are three major types of integral systems which are mutually incompatible. NNN (New Nordic Norm) is a system in which the three holes in front of the boot toe are replaced by a horizontal metal rod which is locked into the binding by a lever. The heavier-duty NNN-BC (Back Country) system moves the rod under the toes, rather than in front of it, which many find to be more comfortable than either standard NNN or three-pin systems. Both NNN and NNN-BC boots and bindings are made by a variety of companies. The third system is Salomon's Profil system, a version of which is used by most racers. They also make a backcountry version. Profil, like NNN-BC, has the pivot point under the toes rather than in front of the boot. A few other companies make Profil-compatible boots. All three of these systems partially interlock the sole of the boot with the surface of the binding under the foot, reducing or (for the Profil) eliminating the role of the heel plate. You must use a boot compatible with your particular binding type.
Telemark bindings are available in two basic design styles, the 75mm Nordic Norm and the NNN-BC. Boots designed for one system are not compatible with the other.
The 75mm Nordic Norm telemark bindings are designed to accommodate the large square toe of a telemark boot. Two basic binding types exist. The three pin binding consists of a 75mm toe piece with three vertical pins protruding off of the base and a sturdy metal bale that clamps the boot onto the plate and pins. When using this type of binding, be careful to ensure that the pins are inserted into the holes on the boot toe. The other binding type consists of a 75mm toe piece and a cable that forces the boot forward and into the binding. There are also bindings with both pins and cables. Both binding types are accompanied by a small heel piece design to keep the heel from slipping. Which binding type you use depends on your personal preference and pocketbook. The cable bindings are generally more expensive, but since they don't use pins they are less damaging to the boots.
The NNN-BC binding system can also be used for telemark skiing with NNN-BC boots, but generally the NNN-BC system is not available with heavy telemark equipment. Opinions about whether it will be available in this type of equipment and how well it performs are mixed.
In addition to the bindings, devices can be purchased which allow the ski to release during a bad crash. The effectiveness and need for these devices is a hotly debated topic, but they may save your knee from a surgeons blade.
Alpine touring bindings are a hybrid of free heel and alpine bindings. They are designed to be used in one of two modes, climbing and skiing. In the climbing mode AT bindings are free in the heel and hinge at the tip of the boot toe so the heel can lift. AT are also equipped with heel "lifters " which attempt to keep the boot heel and toe level while climbing. In skiing mode, the heel and toe are clamped down on the ski like downhill ski boots and bindings. Most AT bindings have some ability to release during a fall.
Models of AT bindings exist that are designed for a particular boot and other models exist that will accept any AT boots. AT bindings should not be used with regular alpine ski boots because the release mechanism is designed to use a Vibram soled boot.
For an overview of alpine gear, see the rec.skiing FAQ. Alpine bindings have improved greatly in the last 20 years, but for backcountry use they still clamp your heel to the ski and so they are not easy to use when hiking. Fortunately for alpine skiers, a recent addition to the spectrum of backcountry gear is a hinged device which fits into alpine bindings and allow alpine skiers to hike with more comfort in their boots, bindings and skis.