Do aircraft have accelerometers?
Most modern aircraft, which includes long range airliners since around 1970, all airliners since not much later, and basically anything with glass cockpit, do have very accurate accelerometers for all three axis, as part of the inertial reference system. 

They are important instruments for the autopilot, as they provide faster feedback on the effect of control deflections than the air-data references, and essential for navigation as cross-reference for detecting GPS errors and the inertial navigation serves as a backup for GPS (and served as primary navigation over the oceans before wide GPS availability). Airbus (since A320) even defines the pitch command by vertical acceleration in the normal law. And yes, they are also used for detecting hard landings and their severity.

The pilot never sees the direct accelerometer output except in fighter and aerobatic aircraft though (well, almost never; there are a couple of other cases).