Getting the right running shoes for your foot type is one of the most important steps you can take to run comfortably and injury-free.
If you have flat feet, you most likely overpronate, which means that your feet roll inward when you run. People with flat feet need running shoes that maintain their stability. When shopping for running shoes, you should look for the words "motion control" and "stability" on the box of running shoes you are considering.
Here are some excellent choices for women with flat feet:

Photo courtesy of PriceGrabberIf you have low arches and are looking for a very stable training shoe, this is an excellent choice for you. The shoe has a broad base that provides amazing support and responsiveness.

Photo courtesy of PriceGrabberThe Saucony Grid Stabil is a very supportive shoe, with a great combination of cushioning and stability. It also has open, breathable mesh to prevent your feet from overheating.

Photo courtesy of PriceGrabberThis is a great running shoe for female runners with a small or medium frame. It has good shock absorption and cushioning, but also provides plenty of support.

Photo courtesy of PriceGrabberA great motion-control shoe, the Brooks Addiction running shoe is a good choice for moderate to severe overpronators. It's very lightweight, but absorbs shock and stabilizes the foot well.