What all you decide may be necessary could depend on how long you are going to be out on the road. Right now I am out for four months. Because of that, I want many things to repair or replace just about anything. I have a tool box in the back of the truck all the time anyway, as this is my daily truck at home around the horse stables, so I keep all manner of tools and hardware with me so I don't have to run back to the shop constantly.
Having tools with you that you may not be able to use yourself may in fact come in handy while you are out, because sometimes a helpful person that offers assistance may in fact know how to use it.
If I listed all the tools I have in the truck and trailer, it would be a rather long list. It is one of the many reasons I prefer a pickup truck compared to a car or suv..... I have more capability to carry the things I need to solve problems.
Suffice to say an extensive collection of handtools, a drill, drill bits, and most everything that has already been listed in this thread.
EDIT: Something I am not sure been mentioned, I carry a 8' extend-a-step ( i think thats what its called ) ladder, so I can get up to clean off the top of the slide, or get up and do any maint on roof seams, etc.