EVERY tool in my shop would be hard to live without. It would mean farming out a lot more repairs. Like working on my cars, fixing things that break etc.
So heres a small list
Aside from the obvious hand tools (wrenches, pliers, screwdrivers, sockets, etc)
Air compressor and air tools
Vise
Welder
Torches
Floor jack/jack stands
Drill
Saws
Good fluke meter
And when it comes to woodworking (not the tedious kind) but framing/building/decks, etc
I absolutly could not live without my sliding compound miter saw. Once you use one, you will almost NEVER use a circular saw again unless you are ripping plywood or something. And mine was just a cheapie menards tool-shop brand 10" single bevel slider with stand for $139 on sale.
It has already built 3 pretty large decks (12x16, 12x20, and 10x20) blus countless other things like shelving and benches in the garage. I definatally got more than my money back out of it.
And when it comes to building/framing things, I could also probabally not live without my transit, 4' level, t-square, and a good tool pouch.