From The Online Etymological Dictionary: c.1380, used first of Germans generally, after c.1600 of Hollanders, from M.Du. duutsch, from O.H.G. duit-isc, corresponding to O.E. þeodisc "belonging to the people," used especially of the common language of Germanic people, from þeod "people, race, nation," from P.Gmc. *theudo "popular, national" (see Teutonic), from PIE base *teuta- "people" (cf. O.Ir. tuoth "people," O.Lith. tauta "people," O.Prus. tauto "country," Oscan touto "community"). As a language name, first recorded as L. theodice, 786 C.E. in correspondence between Charlemagne's court and the Pope, in reference to a synodical conference in Mercia; thus it refers to Old English. First reference to the German language (as opposed to a Germanic one) is two years later. The sense was extended from the language to the people who spoke it (in Ger., Diutisklant, ancestor of Deutschland, was in use by 13c.). Sense narrowed to "of the Netherlands" in 17c., after they became a united, independent state and the focus of English attention and rivalry. In Holland, duitsch is used of the people of Germany. The M.E. sense survives in Pennsylvania Dutch, who immigrated from the Rhineland and Switzerland. Since 1608, Dutch (adj.) has been a "pejorative label pinned by English speakers on almost anything they regard as inferior, irregular, or contrary to 'normal' (i.e., their own) practice" [Rawson]. E.g. Dutch treat (1887), Dutch uncle (1838), etc. -- probably exceeded in such usage only by Indian and Irish -- reflecting first British commercial and military rivalry and later heavy Ger. immigration to U.S.

The word 'Dutch' comes from Old German and is basically the same as the Old German for 'German': deutsch. Over the years the word has evolved a little like most words (Angleland into England). The reason for this is simple; before 1581 the Netherlands were part of the Holy Roman Empire or more specifically part of Germany. The people from the Netherlands were Germans and as such they are still called Germans today.

This is all guesswork and assumption: The Netherlands were originally called the Dutch Republic. Before that however, that area was just a bunch of broken up provinces ruled over by the Holy Roman Emperor. The area was somewhat united by Spain too. Spain at the time was having a collapse of their economy, so the Dutch revolted and took the land for their own. So, thus led to the creation of the Dutch Republic (Why it is called that I don't know). The Republic enjoyed a very wealthy and powerful economy. They were self sufficient. After 204 years (to be exact), the Republic was no more. Four more other governments followed, but were not so stable and did not last for so long. Now after those other governments, the new Kingdom of the Netherlands was created (again, why its called the Netherlands, I am not sure). The name of the 'Dutch' has probably just followed that area since it was called the Dutch Republic. A name lasting for 426 years.

It's only the English language which refers to people from The Netherlands or the language spoken in The Nertherlands as "Dutch". Here's a very clear explanation from WikiPedia: The Dutch refer to their language and themselves as Nederlands. This name is drawn from the name of the country, Nederlanden, "Low Countries", but only since the 19th century replaced the earlier and more common names: (northern) Nederduits and (southern) Diets (Dietsch). In English, however, the language and people are still referred to as Dutch, a word derived from Middle Dutch duutsch, dūtsch but applied originally to continental Germanic speakers, be it of Dutch, Low German, or German proper. By 1600, it had come to be used exclusively for the Dutch after the Netherlands became a united, independent state and the focus of English commercial rivalry.