Not specifically a bug out bag, but here's some of the 'emergencies' that I have run into while in a 4x4 in the woods and what I needed:

1. a stick on the trail rocked up from underneath my truck and broke my fanbelt (yes, even with my factory installed skidplates). Needed a spare fanbelt and hand tools
2. Sharp rock lacerated my fuel tank, needed a sheet metal screw,a washer, a screw driver, and a rubber patch...used a slice of rubber off of the sole of my shoe
3. got high-centered on a concrete firetower pylon concealed in high grass (long story). Needed high lift jack with proper attachments for the vehicle, and some logs for under the wheels.
4. got stuck in backwoods river mud. Needed a hatchet and a jack to cut brush for a base for the tires.
5. tree fell across the backwoods tote road trail in a sudden windstorm. Needed a bowsaw and a tow strap to drag the tree to get out
6. flat tire while parked in a clearing and I was out on a trail. Needed spare and a means for soft-surface jacking.

If you are going to spend a lot of time in the backcountry you should have some robust tools in addition to your survival equipment:

a real shovel (not a little one)
axe, machete, and bowsaw
spare fuses, hoses (esp. lower radiator) and fanbelts
Hi-Lift jack with cover, mount, and proper accessories for your vehicle
heavy nylon snatch strap
good quality lever winch (come-along) or if you have the means, a receiver-mounted winch and a 2" receiver installed in the front and back