There are certain poets who are known for thier sad and dark poetry, like Sylvia Plath and Edgar Allan Poe, and some poets who people forget about, or have no idea that they have written some of the saddest poems out there because its not usually thier genre, like Pablo Neruda or Edna St. Vincent Millay.
With poems with such titles like "Conversation Among the Ruins", and "Suicide off an egg rock", Sylvia Plath become the queen of sad poetry. Depressed most of her life, she killed herself at the age of 30. Although some might say she is overrated, they can't deny the genuine emotion she conveys in her poems. Edgar Allan Poe is also extremely well known. But with lines like "They weep:- from off their delicate stems perennial tears descend in gems", Poe is one of the best to read when you're in that bad mood you just can't shake.
Emily Dickenson also wrote some of the best breakup poetry you can get anymore. The best thing about Dickenson is that she did not mince words, she was straightforward and her message is easy to understand (ex: the poem "Heart, We Will Forget Him"). William Butler Yeats has also written some great poetry, such as "When You Are Old". "Endymion" by John Keats is a bit lengthy, but will definatly make you sob. John Donne is another one to look up when you're feeling sad.
The best way to find some sad poems is just to google them, you'll never know what you'll find. But if you want some specifics, try looking up: Lord Byron, Oscar Wilde, Sappho, Pushkin, Charles Bukowski, Robert Frost, Dylan Thomas, and T.S. Elliot.