Size: It is suggested to be at least the size of an elephant, and a hint can be taken from its name which means "One who stops the flow of rivers" in the native Lingala language.
Appearance: Many descriptions describe the creature as having a huge body, long neck, and a small head, giving the animal an appearance not unlike the classic Sauropod dinosaur. Physical descriptions are also enhanced by the fact that in this case, early explorers took picture books with them to let natives point out similar creatures, and many native tribes did pick out the picture of a Sauropod as being Mokele-mbembe.
Threat: Low. Some reports blame the creature for flipping boats, but they are generally a result of the creature's passing, and not done out of any malicious nature or intent to harm, though like all animals, it can be aggressive if threatened.
This isn't an animal you're going to come across in just any river though. Reports come solely out of the depths of the Congo jungle, where the creature hides under the waters of the river, only coming out to feed on the trees which overhang the water.
Stories of the creature have been attracting attention for well over two-hundred years now, the first known record of it being in 1776 by a French missionary who discovered tracks of an unknown creature which were three feet across. In 1919, an expedition sent into Africa by the Smithsonian Institution to collect plant and animal specimens also reported giant tracks that they were unable to identify, along with roars and sounds which they could attribute to no known animal. More recently, expeditions have been done for several television shows, including Monsterquest, Destination Truth, and Beast Hunter.
While the idea of a living dinosaur is certainly an interesting and beloved one, the idea that a land-based dinosaur surviving through the ages is about as remote as it gets, especially one of this size and type. To have survived through all the various ice ages, changes in weather patterns, through the evolution of the plants it eats and the diseases to which it is exposed (to say nothing of being able to survive contact with man) are odds that would quickly make you rich in Las Vegas. Most likely, it would be a good example of convergent evolution, creating a creature which appears similar to a Sauropod, while not actually being a species of dinosaur which has survived. My guess would be that this is a creature completely unknown to science or a large species of undiscovered elephant.
The Mokele-mbembe has had a fair amount of use as a device in older movies and books. Many of which use it more as a footnote in tales of exploration in the dark jungles of Africa than as a goal in and of itself. The most well known of stories involving this particular creature is probably the 1985 film, Baby, Secret of the Lost Legend. While a good movie, it is very hard to find, as it hasn't made the jump from VHS to DVD. I do recommend it if you can find it though.
Still, wouldn't be a bad idea to keep your eyes open and watching the water if you happen to find yourself floating down the Congo river this summer.