The soleniod contacts are notorious for going bad, giving a click and no starter motor response. Turn the key off, turn it back on, and it may click again, or it may finally decide to catch.

Ignition switches are another source of problems. If there is no clicking of the starter solenoid, electricity isn't even getting down to the solenoid, and the ignition switch is the likely culprit.

'97 T-100 SR5
'86 Toyota's, the variety pack (all gone)