What are the lower and upper hearing limits of the human ear?
Short answer
Hearing threshold is 0 dB SPL at 1 kHz, and pain threshold is around 125 dB SPL at that frequency.

Background
Loudness thresholds depend on acoustic frequency (pitch), as depicted in the following figure:


Loudness contours in human. Source: Stanford Uni

When expressed in dB sound pressure level (dB SPL) the threshold of pain is approximately 125 dB SPL. The lower bound peaks at a hearing threshold of about -5 dB SPL at 4 kHz (maximum sensitivity). Outside that frequency, hearing sensitivity declines (and threshold hence increases).

Note that dB SPL references to a sound pressure of 20 µPa = 2 × 10−5 Pa. This sound pressure corresponds to the hearing threshold at 1 kHz and is hence defined as 0 dB SPL. (Stanford Uni).


Further reading
Why do humans hear better between 2kHz and 5 kHz