Android check device running time since last reboot

Per the answer to this other question:

Go to Settings>About Phone>Status and scroll to the end of the options. You'll see the up time.

From: http://developer.android.com/reference/android/os/SystemClock.html

SystemClock.elapsedRealtime()

elapsedRealtime() and elapsedRealtimeNanos() return the time since the system was booted, and include deep sleep. This clock is guaranteed to be monotonic, and continues to tick even when the CPU is in power saving modes, so is the recommend basis for general purpose interval timing.