A picture of the 1909 replica of the famous CLERMONT.

The name of Fulton's first steamboat is often given as the Clermont. In fact, he never called it by that name, generally referring to it simply as the North River Steamboat, but the name often appears in the literature. (Clermont was the name of the home of his partner, Mr. Livingston, located 110 miles [177 km] away on the Hudson River to which the steamboat traveled on its initial voyage. The trip to Albany continued after 20 hours were spent at Clermont). The Clermont left New York City for Albany, New York on the Hudson River on August 17, 1807, inaugurating the first commercial steamboat service in the world. The initial voyage of Fulton's monster was described as follows in an 1870 publication.

The surprise and dismay excited among the crews of these vessels by the appearance of the steamer was extreme. These simple people, the majority of whom had heard nothing of Fulton's experiments, beheld what they supposed to be a huge monster, vomiting fire and smoke from its throat, lashing the water with its fins, and shaking the river with its roar, approaching rapidly in the very face of both wind and tide. Some threw themselves flat on the deck of their vessels, where they remained in an agony of terror until the monster had passed, while others took to their boats and made for the shore in dismay, leaving their vessels to drift helplessly down the stream. Nor was this terror confined to the sailors. The people dwelling along the shore crowded the banks to gaze upon the steamer as she passed by.
 
The world's first steam warship, the 1814 Fulton the First, also called Demologos, in New York harbor.Fulton patented his design for a steamboat on February 11, 1809, built more steamboats and designed the first steam powered warship, the Fulton the First. The keel was laid in 1814, but he did not live to see it completed.

(This text is courtesy of Wikipedia and comes from an article there about Robert Fulton; GNU Free Documentation License.)