Jamison in the chapter on Artists in Manic Depressive Illness (1990) writes that of 36 American poets in the most recent Oxford Anthology of the time, more than a fifth exhibit well-documented histories of manic depressive illness severe enough to have warranted at least one hospitalization: namely, Hart Crane, Theodore Roethke, Delmore Schwartz, John Berryman, Randall Jarrell, Robert Lowell, Anne Sexton, Sylvia Plath. Of these five committed suicide.
Among the romantics, of course, we need only think of Shelley, Byron, Coleridge, Clare.
In the 18 century, the so-called "Age of Reason", we have Christopher Smart, William Collins, William Cowper, Robert Fergusson, Thomas Chatterton, and William Blake, to name a few likely candidates.
Of course accounts are purely anecdotal about these fellas, plus of course their literary traces. These do provide quite strong indications, however...
Are poets more likely than others to have bipolar affective disorders, as they are called? Assuming a general population rate of 1 to 2 percent, well, it's a question that scarcely needs to be asked. And its almost a tautology to show, as Jamison does, that poets as a group are more likely live out (and die out of) these conditions than biographers or research scientists.