My 1991 Volvo 240 would shut off while driving, but would always restart. This morning it won't turn over. I noticed that the headlights flash systematically while I'm trying to start it. Not sure if that's a diagnostic tool or not. Any idea what might be wrong?

According to my wiring diagram, the headlight switch works a relay which is powered by two different fuses.
I would check the relay for voltage first.
You may need a repair manual to trace the circuits.

I have had this happen before - this is the multifunction switch on the steering column. The one on my Ford took about 10 minutes to change (two bolts). My problem - I would turn my lights off, then turn them back on and nothing, then they would suddenly pop on. after a bit my lights would not come on at all. I had to drive with my Flash to Pass lights for a couple of days when driving at night.

I hope this helps!

you have the wrong light bulb

sounds like it is time to replace the combination/light switch.

This sound like the overdrive relay. try to reset the relay. It looks like this one. I am in no way affiliated with the site my brother had the same problem with his Volvo

Morning, go on craigslist//select Los angeles// scroll down to parts//punch volvo// you will see volvo land in sunland, ca. they have it.

Morning, I found your problem...its going to be your fuel pump. Allow me to explain. When you start your car in the morning the car starts just fine. As your driving the fuel pump will eventually get hot. Therefore the circuit cuts off when you turn off for a while then you jump back in to restart the vehicle and it doesn't. The reason is when the fuel pump gets hot it shuts off due to circuit wire inside the pump.
You can almost say like overheating. Therefore your pump is going out. Replaced 7-10 of them in my time as a mechanic. Do yourself a big favor. Don't get a used on or Autozone. Pep boys or Napa will do just fine. Goodluck.

Try the headlight relay. It is behind the kick panel directly in front of the driver. It might be shorting on the wiper relay which is in the same location. 

keep the fuel tank at least half full.....it may helps cool the pump

Have you ever change the fuel filter? if not then try this