The 2001 National Household Transportation Survey ... showed that, on a typical day, when household members shared a car men were more than three times more likely to be the driver as opposed to a passenger.
This an issue in our family. There are three female drivers in the Gruntled family now, and they all almost always prefer that I drive. I always ask Mrs. G. (we were trained as '70s feminists in gender power, after all) and she almost always asks me to drive.
I can think of two reasons for the gender imbalance in who drives, both well rooted in sex differences.
First, men as a group find spatial problems easier to solve. So if we are taking a trip that might include parallel parking, the ladies in our family would rather that I handled it. This varies quite a bit from individual to individual, so your mileage may vary. Still, the sex difference in handling spacial issues is well-attested, so it should show up as a tipping factor in some driving decisions.
Second, women like to look at their conversation partner when talking, whereas men often do not. If she is driving and talking to him, she may often turn to look at him to see his reactions. Taking her eye off the road while driving is scary to both of them. On the other hand, if he is driving and talking to her, she can look at his face without danger, while he will be much less tempted to swivel to look at her at each turn in the dialogue.