Some English language words have letters with diacritical marks. Most of the words are loanwords from French, with others coming from Spanish, German, or other languages. Some are however originally English, or at least their diacritics are. Proper nouns are not generally counted, except when used as an eponym.
The trend to drop diacritics is much stronger in U.S. English than in British English. The current state changes from one edition to the next of all dictionaries. Generally speaking, if one wants to make a “good impression” (show that one is "educated"), it is better to use the diacritical form unless one is an expert in the field and knows whether it is already considered acceptable to drop the diacritic . On the other hand, one can decide to purposely make a self-assured and "modern" impression by trusting to one’s feel for the language and using spellings without diacritics (perhaps in connection with something blatant like a so-called split infinitive to show that the diacritic was left out on purpose).
Diacritics appear to be more acceptable in Canada than in the US, where anglophones are used to seeing French on food packaging, and French words often retain their orthography, for example café, Montréal, née, Québec, and resumé.
In German words, the letters with umlauts ä, ö, ü may be written ae, oe, ue. This could be seen in many newspapers during World War II, which printed Fuehrer for Führer. However, umlauts are usually now left out instead, with no e following the previous letter.
Occasionally, hypercorrection can occur with borrowed words, with diacritics added where there should be none, in the erroneous belief that this is the correct form. An example is the addition of an accent to the e in latte, to become latté or even lattè. In Italian, where an accent (almost always a grave accent) is used to indicate stress on the final syllable, latte is stressed on the first syllable, so has no accent. However, confusion with French café or Italian caffè leads to the unnecessary accent being added. These cases when the diacritic is not borrowed from any foreign language but purely of English origin, include the ö in the rare variant spellings of words such as coöperation (compare the original French coopération) and coöperative (e.g. the Harvard/MIT Coöperative Society).