The Oort Cloud may account for a significant fraction of the mass of the solar system, perhaps as much or even more than Jupiter. (This is highly speculative, however; we don't know how many comets there are out there nor how big they are.)
The Kuiper Belt is a disk-shaped region past the orbit of Neptune roughly 30 to 100 AU from the Sun containing many small icy bodies. It is now considered to be the source of the short-period comets.
Occasionally the orbit of a Kuiper Belt object will be disturbed by the interactions of the giant planets in such a way as to cause the object to cross the orbit of Neptune. It will then very likely have a close encounter with Neptune sending it out of the solar system or into an orbit crossing those of the other giant planets or even into the inner solar system.
There are presently nine known objects orbiting between Jupiter and Neptune (including 2060 Chiron (aka 95 P/Chiron) and 5145 Pholus; see the MPC's list). The IAU has designated this class of objects as Centaurs. These orbits are not stable. These objects are almost certainly "refugees" from the Kuiper Belt. Their future fate is not known. Some of these show some cometary activity (ie, their images are a little fuzzy indicating the presence of a diffuse coma). The largest of these is Chiron which is about 170 km in diameter, 20 times larger than Halley. If it ever is perturbed into an orbit that approaches the Sun it will be a truly spectacular comet.
Curiously, it seems that the Oort Cloud objects were formed closer to the Sun than the Kuiper Belt objects. Small objects formed near the giant planets would have been ejected from the solar system by gravitational encounters. Those that didn't escape entirely formed the distant Oort Cloud. Small objects formed farther out had no such interactions and remained as the Kuiper Belt objects.
Several Kuiper Belt objects have been discovered recently including 1992 QB1 and 1993 SC (above). They appear to be small icy bodies similar to Pluto and Triton (but smaller). There are more than 300 known trans-Neptunian objects (as of mid 2000); see the MPC's list. Many orbit in 3:2 resonance with Neptune (as does Pluto). Color measurements of some of the brightest have shown that they are unusually red.
It is estimated that there are at least 35,000 Kuiper Belt objects greater than 100 km in diameter, which is several hundred times the number (and mass) of similar sized objects in the main asteroid belt.
A team of astronomers led by Anita Cochran report that the Hubble Space Telescope has detected extremely faint Kuiper Belt objects (left). The objects are very small and faint perhaps only 20 km or so across. There may be as many as 100 million such comets in low-inclination orbits and shining brighter than the HST's magnitude-28 limit. (A follow-up HST observation failed to confirm this observation, however.)
Spectra and photometric data have been obtained for 5145 Pholus. Its albedo is very low (less than 0.1). Its spectra indicates the presence of organic compounds, which are often very dark (e.g. the nucleus of Comet Halley).
Some astronomers believe that Triton, Pluto and its moon Charon are merely the largest examples of Kuiper Belt objects. (But even if this is true, it will not affect Pluto's official designation as a "major planet" for historical reasons.)
But these are more than distant curiosities. They are almost certainly pristine remnants of the nebula from which the entire solar system was formed. Their composition and distribution places important constraints on models of the early evolution of the solar system.