Comet Periodicity
Most comets have an elliptical orbit around the Sun, whose period can vary enormously. Comets are generally defined as being short-period if their orbit is less than 200 years, the remainder being known as long-period comets.
Short-period comets tend to remain within the orbit of Jupiter and close to the plane of the Solar System ecliptic. The shortest known period is Encke's comet, which orbits every 3.3 years. The long-period comets may have an aphelion well outside the orbit of Pluto and can be inclined at all angles to the plane of the ecliptic. These are sometimes thought of as belonging to Jupiter's family. B. G. Marsden's Catalogue of Cometary Orbits (1972) lists 97 short-period comets and 503 long-period ones.
Other comets are not orbiting the Sun at all, and move in on hyberbolic paths, only to disappear again. For others, their orbits are too long to calculate - possibly disappearing for tens of thousands of years.
Naming
Most comets are named after their discoverers and denoted by letters in the order of discovery (see Amateur Astronomer for examples). After that, they are numbered in order of their perihelion passage (for example, the Arend–Roland Comet was 1956h but became 1957 III). New comets are being discovered at the rate of 10-12 a year, many of them by amateurs.
Sub-types
Astronomers have come to the conclusion that there may be two distinct types of comet - one rich in methanol and one low in methanol. This is supported by observations of the spectrum of Comet Hyakutake. The continuing study of comets will undoubtedly add to our understanding of the nature of our own solar system.