If you're looking for specific running shoes designed to be therapeutic for plantar fasciitis and correct typical foot irregularities, you may find the section on running shoes helpful in Shoes for Plantar Fasciitis. I can also tell you that a popular shoe for overpronators with flat feet is the Saucony Women's ProGrid Stabil CS Running Shoe (or the men's version for guys).
If you're interested in my experiences and what I've learned from research, read on.
I found a nice summary page at the Hospital for Special Surgery in New York on how to find the right running shoe. It has all the standard stuff you should know for choosing athletic shoes and describes how to check a shoe for stability and flexibility, how to determine your foot arch, and more. It doesn't, however, cover much about shoes for plantar fasciitis in particular. This information is often too complex to cover in simple online articles because it depends so much on your particular feet and stride.
Personally, I've had so-so luck with running shoes as far as my plantar fasciitis goes. Generally, athletic shoes don't offer enough support for me, so it's a given that I have to switch out the useless insoles they come with with my Sole footbeds.
The pair that seemed to help me for a time was the Brooks Adrenaline, but it turned out that I was looking at the wrong type of running shoes. I'd been led into thinking I was an overpronator, and I no longer think I am. The Brooks Adrenaline slowly made my feet hurt in other ways, even if they didn't bring back my plantar fasciitis. (I recently came across this excellent article discussing pronation and supination and the mistakes often made by running shoe "experts," written by a physical therapist.)
When I had my most recent bout of plantar fasciitis that wouldn't go away, I looked for advice. A funny thing, here - I'd written an article on the best footwear for plantar fasciitis. Over 4,000 people had responded to a poll I'd put up, and now I sought advice from them. New Balance turned out to be the reader favorite; it got the most votes.
So I ordered some running shoes online. I tried models New Balance 576 and New Balance WR883 and the Brooks Dyad 6. They are all neutral running shoes, for people who neither overpronate or oversupinate.
With the Sole custom insoles inserted in them, they were comfortable enough, but they didn't succeed in getting rid of my plantar fasciitis. I ended up keeping the cheapest one, the 576 that I'd gotten on sale, and sending the others back, as they all felt pretty much the same to me.
I haven't worn these New Balance for running at all (my knees won't take that anymore), nor have I worn them very much since I healed up (you can see my Strassburg Sock review on how I "cured", so to speak, this latest bout of plantar fasciitis.) My athletic life is pretty much on hold these days, so I've been wearing my London and Haflinger clogs most of the time. I'll try to report back on how these New Balance shoes hold up as far as preventing my plantar fasciitis from recurring after I get some real mileage in them. (OK, I've finally worn them for an entire day and wasn't too happy - see my post reviewing them.)
For people with high arches who underpronate, I also wrote an article called the Best Running Shoes for Supination.