2004 Dodge Durango CEL comes on for seemingly no reason

Why does the check engine light come on in my 2004 Dodge Durango when there seems to be nothing wrong?

You need to have the codes read to find out.

The Powertrain Control Module is more sensitive to failures than you are.
Cycle the ignition switch from “off” to “run” (not start) three times, the third time leave the switch in the run position and read the fault codes displayed in the odometer display.