While I took enough shop in high school to rebuild a carburetor on the side of a road (and I've done it with my older vehicles), these newer vehicles are #1, more reliable, and #2, more difficult to fix. That's why I focus on the most likely things to go wrong and my tool kit is pretty minimal (screwdrivers, adjustable wrench, small vice-grip). What I do carry is spares for what I can fix:
Fix-a-flat (in case it goes flat some place that would be dangerous to change, I have multiple flats, or discover a flat spare)
Jumper cables or a jumpstarter/inverter/compressor/usb charger (cables in the car, jumpstarter in the truck)
Duct tape, electrical tape, bailing wire
Tow strap (even in my little car, because that guy in the big truck might not have one, but he's always willing to show off how hard his truck can pull on things)
Insulated wire (10-12 ga)
Breaker bar for tire wrench (handy for some other things, too

)
Spare wiper blades (at least the driver's side)
Spare headlamps (at least the low beams)
Windshield washer fluid
Quart of oil and ATF
Tire chains (I keep mine with my spare year-round)
Fuses
Also useful:
High visibility vest (not only for the side of the road, but serves as an all-access pass in many emergencies)
Rain gear you can work and walk in (and enough disposable ponchos or garbage bags for every occupant of the car)
Get Home Bag (similar to a BOB, but be sure to include good walking footware, winter clothing and keep it light and portable)
Latex/Nitryl gloves
Rags or paper towels
Cheap, disposable wool gloves (army surplus liners) (thin enough to work in, thick enough to keep your hands off cold tools)
Ratchet straps (the 10,000 pound rated ones can work as a come-along in a pinch)