Your starting problem could be a weak fuel pump, or it could be caused by a patially clogged fuel filter. The best approach would be to have a garage run a pressure test on your fuel system, this will tell if you are getting correct fuel pressure to the injectors. If the pressure is low it can cause starting problems, this can be caused by a partially clogged filter or a defective fuel pump. The fuel filter is an an easy inexpensive fix, the fuel pump considerably more expensive. The gas tank has to be removed to replace pump. also these pumps are not cheap, they cost over a hundred bucks and up. So considering labor to remove and replace tank plus a new pump you are looking at a fairly expensive repair if a new fuel pump is needed.

Iggie,
Thanks for the advice. That gives me a much better idea of what the problem probably is. I should do something about it soon too, since I imagine the problem will only get worse as the weather gets colder. Here's hoping that it is just the filter!
Audrey

You might want to take what Chad says with a grain of salt.
( about a pound ). I had a 1986 Taurus in the yard with a
PLUGGED filter. So plugged that the key had to be turned
on and off 3 times to even get enough gas to fill the
injectors. no way in hell would that engine start without
3 or 4 primes.After it was warm it was fine. The filter was original and still tared into the frame. It weighed about 3 pounds when i took it off. It also took out the fuel pump because of the exessive back pressure. If gas was so clean these days why do they still use filters and why do they weigh about 3 - 4 pounds if left in for a few years ? Try the filter first. It's the cheapest why to go.
If it is the filter and plugged that bad your pump is not long for this world. Good luck

Thanks, everybody, for your comments. I have to take the car to a Ford garage soon anyway for a recall--something to do with the Speed Control Deactivation Switch. But I think I'll wait until the parts are actually available to fix that, which I was informed wouldn't be until the fourth quarter of this year. (I'm assuming that means October!) I'm hoping I can ask them to figure out what is causing the starting problem at the same time.

My dad kindly took the Crown Victoria to a local Ford garage for me. They replaced the fuel filter and cleaned something called "the throttle body and air by-pass valve." So far the car seems to be starting well and the total cost came to less than a hundred dollars--most of that for labor. The only downside is that they didn't yet have the parts for the recall (to fix the speed control switch). But, since I don't use the speed control very often anyway, it's not really much of a problem. Thanks again to those of you who made helpful suggestions!