This just started last night. My wife was driving home and on 3 occassions, the lights started dimming and no matter how hard she pushe the gas, it would do nothing. Then suddenly it would surge back to life for a little bit before doing it again. I took it out after she got home and almost immediately it started doing it. I tried to limp it home and it stalled and would not start again. I pushed it home and tried it again about an hour later. It ran, poorly, for about 30 seconds before dying. Now it won't start at all. I checked fuel pressure in the daylight today and it was at about 6 psi, way too low. I turned the key to on where the fuel pump should prime the system and not only did the pressure not change, there was no sound from the pump. At this time I'm 95% certain it is the pump that went to hell, but I just want to verify that there isn't a common relay or resistor or something that fails with any regularity.

This is a 1996 Bonneville SE with about 250k miles, usually runs great. Tune up about 5k miles ago, no check engine light, even when it is in the process of stalling.

You may want to check your connections at the positive battery cable just for piece of mind. I've had some stalling troubles, and in my case they were due to corrosion in and around the cable ends. Caused stalling and occasional no-start.

Not enough volts will cause all sorts of wierd things to happen with these cars.

6 psi at the rail is a problem with the filter, fuse, wiring or pump itself. My 90 has a fuel pump test connector near the positive batt terminal. Not sure where the 96 is.
If its an original pump it could have seen better days, but its best to test it out.