Looking at the responses, the screwdriver issue can often be nicely
met with one of those 6-in-1 screwdrivers. It has 2 slotted bits, #1 &
#2 Phillips, and the sockets for the bits take care of the two most
common hex heads for things like sheet metal screws. I keep one of
those in every toolbox in addition to the usual screwdriver set. Also,
a small set of "jeweler's" screwdrivers is mighty handy for glasses.
Even the "emergency" kit you can get in the drugstore is handy.

When traveling (need to put in checked baggage), a multi-tool and/or
Swiss Army knife is a good bet. Swiss Army knife in the glove
compartment of the cars, for sure.

The wire stripper/cutter/crimper/bolt cutter is also a handy thing to
have in your tool box.

You also need a tape measure, pencil, and brad awl for marking, or
making starter holes.

Hand drill (really!!) and set of small bits.

Set of Allen wrenches - lots of plumbing fittings have them on the
knobs.

Small flashlight.

They guy that dies with the most tools wins.