I have my big (old) air compressor at my hangar but I don't use it on the plane. I imagined using it for compression checks, which I'm sure will happen when I'm the head wrench turner on my Kitfox. For tires I use an old bicycle pump, and I have two low pressure tire gauges which read low enough I can nail 12psi easily.
As above, a set of combination wrenches and good quality screw drivers hang on my wall. A broom and dust pan get used often. It's crazy how much dirt shows up on the floor of a hangar or garage with the doors closed and no activity.
I have one of those quartz shop lights on a stand, and from it I have an old school drop light. That contraption comes in handy very often and doubles as a source of warmth. I also have a couple of good flashlights and a headlamp. Inspection mirror and magnetic picker upper things are both handy no matter what you're working on.
Microfiber cloths and Lemon Pledge (or suitable high tech replacement) are always needed.
I have a big white board on the wall with a table of numbers showing aircraft TT, engine SMOH, next annual, next oil change, transponder and ELT. It also shows my own currency for BFR, CFI, medical and 90 day tail wheel currency.
I didn't run a dispatch log until I took on my non-equity partner but with both of us flying it was required to keep track of the hours he was flying off.
The white board also serves as a scratch pad where we make notes to each other about fuel or an added quart of oil. I also have a running total of hours per added quart (seems to vary around 10-15 hours/quart).
Now I've got a ton more crap in my hangar but that is my list of essentials. Oh and a comfy chair or two.
