A big +1 for Aryeh Kaplan. He was really the masterworker of Kabbalah and Hasidut in English translation. His translation of the stories of Rebbe Nachman of Breslov is especially phenomenal.
Adin Steinsaltz did a nice collection of Kabbalistic stories called The Thirteen Petalled Rose, and many if not most of those have ended up as Hasidic stories in one form or another.
Reb Zalman Schachter-Shalomi did a very fine introduction to the Hasidic masters and their thought, called Wrapped In A Holy Flame. I believe there is also one called A Heart Afire.
Elie Wiesel's Souls on Fire is a nice little introductory volume.
There is always Buber's Tales of the Hasidim, although I find that to be rather watered-down.
There is a whole English language Chassidus (Hasidut) section at nehora.com, which is my favorite online Jewish bookseller for hard-to-find volumes. They have some really quality stuff there: worth checking out.