I have a 1989 cherokee 4.0L. The fuel pump runs constantly even if the key isn't in the on position. As long as the battery is connected. the pump runs. Why is that? possible Starter Relay? Any other ideas?

fuel pump relay bad

If it's not the relay, something is shortening.

Check the relay as that is the most obvious. If the relais is ok, break out the multimeter and start checking the various wires/circuits.

Jeroen

Yeah, it's probably the shortening. This kind of stuff happens when it needs to be replaced.