A multi-tool is what it sounds like. It's a small, compact tool that has different knife blades, Phillips and flat head screwdrivers, wire cutters and pliers all in one. It's like a Swiss Army knife on steroids. These are essential for stagehands to have, as it keeps you from having to carry around an entire tool box but it will still let you deal with most emergencies backstage.
Gerber and Leatherman are two of the leading makers of multitools, and both make an excellent and durable product.
Many theaters have their own drills, but it's a good idea to bring your own so you won't be waiting to use it if another stagehand gets to it first. You will need them especially if you are setting up scenery or doing any number of light carpentry fixes, such as adding door handles or coat hooks to scenery or screwing steps into place.
An adjustable crescent wrench is an essential tool for the lighting technician. Since almost every lighting unit is hung with a C-clamp, a wrench is needed to tighten and loosen them. Experienced electricians will carry speed wrenches that are designed for the common sizes of bolts on C-clamps and lighting equipment.
It's always a good idea to have a tape measure. Electricians need it to space out the lights on a flying batten. Carpenters need it to measure out the wood. Stage crew may need it to see if a piece of scenery can fit through a doorway and then place it on the proper spot on the stage.
It can get dark backstage, especially when the work lights are off and the show is underway. Your flashlight will help you find your way backstage without disrupting the performance. Maglites are a common brand in the theater, and there are many different kinds of powerful LED flashlights to choose from as well.
Protect your hands! Your hands are your most important tool, so protect them from wood splinters, rope burns and the heat of hot lamps. Gloves should be snug, but not so tight you can't move your hands in them.