One problem with trying to make a dramatic feature film about poets is that most of the drama in a poet's life occurs in his or her head. A second problem, flowing out of the first, is that the film-makers then try to compensate by focusing on sordid details or on cliche aspects of the alleged "poet's life," such as drinking alcohol, being wild, yadda yadda. A third problem is that, probably, no one should try to "dramatize" the writing process. All of that said, here is a list of movies about poets, pretty much in the order they occurred to me, although I do begin with my favorite:
1. Stevie (1978) It presents her life and doesn't try too hard to dramatize poetry and poets.
2. Priest of Love (1981) About D.H. Lawrence. Not bad. Ava Gardner has a role.
3. The Edge of Love (2008) About Dylan Thomas. Falls into some of the traps mentioned above.
4. Dead Poets Society (1989). A favorite of many. More about poetry and teaching than poets. I liked it all right.
5. Panaemondium (2000)About Wordsworth and other British Romantic poets. The scenes that try to portray Wordsworth composing are painful to watch. The stuff about literary politics and Wordsworth's ego is good.
6. Beat (2000). Focuses mainly on Burroughs. It's pretty good.
7. Looking for Langston (1988) Quasi-documentary stressing Hughes's sexuality. A fine film--but it really is only about one aspect of Hughes's life, alas.
8. Total Eclipse (1995) Concerning Rimbaud and Verlaine. Very good. With Dicaprio.
9. Dr. Zhivago (1965). Of course, this movie about a lot besides poetry, but the main character is a poet, after all.
10. Beautiful Dreamers (1990). This is the one among the 10 I haven't seen, but it looks intriguing. It's about Walt Whitman. Not great reviews on IMDB, alas.