The Poetry Archive website has English translations of several of Heine's poems
Atta Troll, 1847 - Atta Troll, A Midsummer's Night Dream
Romanzero, 1851
Der Doctor Faust, 1851
Les Dieux en Exil, 1853
Die Harzreise, 1853
Lutezia, 1854
Vermischte Schriften, 1854 - Various Writings
Letzte Gedichte und Gedanken, 1869
Sämtliche Werke, 1887-90 (7 vols.)
Sämtliche Werke, 1910-20
Sämtliche Werke, 1925-30
Werke und Briefe, 1961-64
Sämtliche Schriften, 1968
Prose Writings of Heinrich Heine, 1973
The Lazarus Poems, 1980
Heinrich Heine: Poetry and Prose, 1982
Religion and Philosophy in Germany, 1986
The Romantic School and Other Essays, 1986
Selected Verse, 1986
Selected Prose, 1993
Songs of Love & Grief, 1995 (a bilingual anthology)

Criticism and Biography:

Cook, Roger F., Ed. A companion to the works of Heinrich Heine. Rochester, NY: Camden House, 2002.
Gelber, Mark H. The Jewish reception of Heinrich Heine. Tubingen: M. Niemeyer, 1992.
Hohendahl, Peter Uwe and Sander L. Gilman, Eds. Heinrich Heine and the occident: multiple identities, multiple receptions. Lincoln: University of Nebraska Press, 1991.
Kossoff, Philip. Valiant heart: a biography of Heinrich Heine. New York: Cornwall Books, 1983.
Nisbet, Delia Fabbroni-Giannotti. Heinrich Heine and Giacomo Leopardi: the rhetoric of Midrash. New York: P. Lang, 2000.
Perraudin, Michael. Heinrich Heine: poetry in context: a study of Buch der Lieder. Oxford: Berg, 1989.
Peters, George F. The poet as provocateur: Heinrich Heine and his critics. Rochester, NY: Camden House, 2000.
Spencer, Hanna. Heinrich Heine. New York: Twayne Publishers, 1982.