About 10% of quasars show Broad Absorption Line troughs from gas in outflows with velocities of typically 0.1c. It is likely that all quasars have BAL outflows, at least at some point in their lifetimes, and BAL mass loss rates are comparable to the accretion rates required to power quasars. Thus an understanding of BAL outflows is required to understand quasars as a whole. The most unusual BAL quasars help us understand the full range of parameter space spanned by BAL outflows. The Sloan Digital Sky Survey has confirmed that populations of unusual BAL quasars exist. These include objects with almost complete absorption below MgII, objects heavily reddened by dust with an extinction curve even steeper than the SMC, possible transition objects between low- and high-ionization BAL quasars, and objects with redshifted absorption troughs (perhaps due to absorption of an extended continuum source by a rotation-dominated disk wind). I will discuss these different types of objects and what they tell us about BAL outflows.