[MENTION=199002]dslrjunky[/MENTION] are you asking about only on-road, or was that a separate question. if you are just asking about on-road driving, unless those roads are in the middle of nowhere the basic kit would just be a cell phone and AAA
regardless of on-road or off-road, i recommend carrying enough supplies for you and any passengers to at least spend the night in the vehicle comfortably (i.e. enough food, water, a couple blankets, etc... and make sure it is appropriate for your climate and location) as well as a change of clothes and some toilet paper/wet wipes.
As far as a first aid kit I think this is really helpful, especially if you have children, but unless you are remote having the bump and bruise type stuff isn't critical since this stuff can wait until you get home or to a drug store or something. I'd recommend getting a tourniquet and knowing how to use it (lots of videos online) for a kit for things that are immediate needs and can't wait and make sure it's easy to get to (at minimum i'd include the tourniquet, aspirin, benedryl, glucose paste, gloves and go from there). I keep a big kit in the back and a trauma kit on the drivers door.
a flashlight or headlight and leatherman-type multi-tool are also very useful for all kinds of things, including non-emergency stuff
from there you can start adding any tools or other things that you want that make sense for where you are and your experience level (i.e. a detailed toolbox is a waste of space if you are in a metro area with AAA and you have no plans to work on the vehicle yourself)