Dead battery: jumper cables
Flat tire: Fix-a-flat, pliers, WD-40
Low oil: 2 quarts oil
Low radiator: bottle of coolant
No windshield washer fluid: bottle of washer fluid
Environmental comfort and safety: poncho, flashlight, batteries, reflective vest or tape, wet wipes, mylar survival blanket, flares or triangles (or is that too much?). Lighter or matches if the flares need them.
Injuries: Some sort of 1st Aid kit. Band Aids and Neosporin for the expected cuts and scratches; large dressings and bandages for more serious burns, trauma (e.g. in an accident).
General: Some amount of cash money. Duct tape. Several large white garbage bags. Folding knife. Black permanent marker.
Emergency preparedness materials suggest keeping 3 days of clothing, water, food and medicines in duffels in both home and car, for every member of the family. I think I'd be running out of trunk space! But maybe some water.