For looking up the time of the next Metro train or nearby buses, I usually stick with WMATA's own site. You have to select a Metro station for train estimates, but the NextBus link works off your phone's location.

As far as apps go, RideScout looks promising--it lets you compare travel times via train, Metro and other bus systems, bike, Capital Bikeshare, taxi, driving, walking--but on Android it's basically the RideScout site encapsulated in an app. The iOS version feels a lot more solid; a "real" Android version is supposed to be on the way.