My current set of tools is as follows, in very rough order of essentialness:
1. #2 Robertson (square drive) screwdriver. This is absolutely essential in my opinion; it's nearly impossible to do any sort of work on the RV without one.
2. #2 Phillips screwdriver (mainly for various screws I've put in, I'm afraid) 3. Utility knife
4. Fini AirBoss air compressor, dually tire chuck
5. Breaker bar, sockets, and bottle jack to be able to put on the spare
6. Adjustable wrench
7. Basic slip-joint pliers
8. Screwdriver/bit set with virtually every bit known to man
9. Electrical tape, Gorilla tape
10. Cheap little multimeter
I'm currently also carrying a larger (#3?) Phillips screwdriver and a nutdriver the size of which I forget especially for tightening the pivot on my driver's side rear view mirror that likes to loosen up over time.
And some things that have been listed by others that I would consider more basic supplies and equipment than tools, but the categories are rather imprecise:
1. Tire pressure gauge
2. Flashlight(s)
3. Wheel chocks
4. Level
5. Broom
6. Hatchet (mostly for making campfire kindling)
7. Spare fuses
8. Graphite for locks (probably not so important for newer rigs)
9. Black tank flush wand