Energy scavenging health monitors are provided for assessing the health of components onboard aircraft and other vehicles, as are methods carried-out by energy scavenging health monitors. In various embodiments, the energy scavenging health monitor includes an energy scavenger system, a controller coupled to the energy scavenger system, and a first sensor coupled to the controller. During operation of the health monitor, the first sensor provides sensor signals to the controller, which are indicative of an operational parameter pertaining to a monitored device of the vehicle. Storage media contains computer-readable instructions, which when executed by the controller, cause the energy scavenging health monitor to determine when a predetermined trigger event has occurred based, at least in part, on electrical input signals received from the energy scavenger system. In response to occurrence of the predetermined trigger event, the controller further stores data indicative of the sensor signals in the storage media.