late 14c., used at first of Germans generally, after c. 1600 in the narrower sense "Hollanders;" from Middle Dutch duutsch, from Old High German duitisc, from Proto-Germanic *theudō "popular, national" (source of Modern German Deutsch), from PIE *teuta- "tribe" (compare Teutonic). It corresponds to the Old English adjective þeodisc "belonging to the people," which was used especially of the common language of Germanic people, a derivative of the Old English noun þeod "people, race, nation."
As a language name, it is first attested as Latin 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 use in 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 German, Diutisklant, ancestor of Deutschland, was in use by 13c.).
Sense in England narrowed to "of the Netherlands" in 17c., after they became a united, independent state and the focus of English attention and rivalry. In Holland, Duits (formerly duitsch) is used of the people of Germany. The old use of Dutch for "German" continued in America (Irving and Cooper still distinguish High Dutch "German" and Low Dutch "Dutch") and survives in Pennsylvania Dutch for the descendants of religious sects that immigrated from the Rhineland and Switzerland and their language.
Since c. 1600, 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 German immigration to U.S.
Dutch concert, a concert in which each one sings his own song at the same time that his neighbor sings his; or a concert in which each one sings a verse of any song he pleases, some well-known chorus being sung after each verse. [Century Dictionary, 1897]
The Dutch themselves spoke English well enough to understand the unsavory connotations of the label and in 1934 Dutch officials were ordered by their government to stop using the term Dutch. Instead, they were to rewrite their sentences so as to employ the official The Netherlands. [Rawson]
Dutch oven is from 1769; OED lists it among the words describing things from Holland, but perhaps it is here used in the slighting sense. Dutch elm disease (1927) so called because it was first discovered in Holland (caused by fungus Ceratocystis ulmi).