Examples of errors:
(1) Other important functions of literature have been existing from their beginning until today.
(2) I'm not thinking a suggestion box would be the right way to change things.
(3) I told myself, "This semester you are intending to concentrate on English."
(4) The times are overlapping, so I couldn't choose all the courses I wanted to.
(5) The tooth consists of two parts, a part outside the jawbone, which is visible, and a part which is lying inside the jawbone and is not visible.
(6) The individual is left alone, and furthermore the principle of competition is dominating in our society.
(7) I'm coming from the Ruhrgebiet.
(8) In America nearly everybody is coming from somewhere else, so everybody has an accent.
Since it is probably possible to construct contexts for every verb where the progressive would be possible, we cannot say that "certain verbs" do not allow the progressive, but rather that certain verbs used in certain senses do not allow the progressive. Be, for example, allows the progressive only in its relatively unusual sense of 'act':
Stop being silly!
Exist (cf. (1)) is another classic example of a stative verb (i.e. one that does not take the progressive), although in the sense of 'survive, subsist'. the progressive is possible, e.g.:
He's famished. He's been existing on nothing but coffee and cigarettes for the last three days.
Come (cf. (7). (8)) in the sense 'originate from, have as a home town or birthplace', doesn't allow the progressive, but it does in its more usual sense of 'approach':
The bus is coming.
Think (cf. (2),) has a more general, stative sense of 'to have the opinion', which does not allow the progressive, and a more specific, active sense of 'meditate', which does; compare:
I think John is a fool.
Leave me alone, I'm thinking.