When I'm in the bee-yard, all I really need is a hive tool, smoker with fuel (Burlap), propane torch to lite fuel, a frame holder, that I hang on the side of hive body, great for putting frames aside for inspections.
I have gobs of stuff which most here mentioned for doing removals, such as queen catchers, queen cages, scrapers, sheetrock saw, hammer, cut-off saw, sawzall, bee-quick, burlap, propane torch, rubber bands, pheremone, swarm traps, 2x 10 sections for putting back 2x 8s, 2x10 & 2x12 sections, nails, thumbtacks, camera, rolls of plastic, bee-vac...