We present the first targeted survey for Extremely Low Mass (ELM) white dwarfs (WDs), helium core WDs with masses <0.3 M &sun;. Such low mass WDs are the signature of extreme mass-loss stellar evolution. We have discovered over a dozen new ELM WDs, most of which are compact binary systems with <1 day orbital periods. We predict that at least one of the systems is an eclipsing double-WD system that we can use to place fundamental mass-radius constraints on helium-core WD models. Intriguingly, the observed ELM WD systems are merging due to gravitational wave radiation and will become gravitational wave sources. We use our well-defined, non-kinematically-selected sample to measure the space density of ELM WD systems; their merger rate is comparable to the rate ofunderluminous supernovae, one model for which is the detonation of 0.3 M &sun; worth of helium.