I feel that the best way to answer this is to more or less copy whatever tools you use at home, excluding special projects (such as remodeling, building furniture, or whatever it is you do for a hobby or necessity). Just the basic things you find handy around the house.
I say this because it really is a personal ability thing really. Why should a completely tool-illiterate non-handy person carry extensive tools?
I recon almost everyone would want basic screwdrivers for changing batteries in remotes and toys, or whatever... beyond that though...
For me, I keep a small-ish tool bag at home. screwdrivers, a complete compliment of pliers (linesman, wire stripper, needle nose, channel locks, different sizes, diagonal cutters, etc...), micro screw driver set, digital mutimeter, electric outlet tester, hammer, utility knife, utility scissors, a few basic box end and adjustable wrenches, some chisels, a nail set, putty knife or two, a small hacksaw, tape, wire nuts, IR thermometer, cordless drill/driver and bit set, a speed square, and more...I even have a romex stripper I tend to keep in there even though it's not an oft used thing. It's my go bag I can tote to where I need to work on something.
I used to just grab that bag and load it in the RV for every trip. I used a lot of that stuff early on when I was chasing through the factory errors and doing a bit of "modding" type projects. Use of course tapered down to once in a while... almost never
Still, I eventually just duplicated that tool bag for the RV. Much of it is much cheaper stuff, some even from harbor freight.
Personally, beyond a few combination wrenches I don't have anything really for the automotive mechanical side of things....no sockets, etc...
I also don't have much in the way of plumbing tools, except for the channel lock pliers.
An auto mechanic on the other hand might want to bring along sockets, jacks, and all sorts of other specialty tools for what they know and do...
An electrician on the other hand would prob bring a much more substantial set of electrical type things.
I've found you can always buy a tool on the road if you need to....