Steel wool (for cleaning nasty slides and valves)
I pull a lot of stuck slides. You can get most of that done with penetrating oil, a torch, and a rawhide hammer. A slide hammer (not your rawhide hammer - a slide hammer is weight that slides along a hook) is useful, and a rag or something else to yank on the slide with.
Before you re-solder a brace or a joint, you need something to hold the parts in place. Ideally that would be a wooden mandrel (a table leg from Home Depot can do in a pinch) held in a bench vise. If that's not possible, you can rig something up with zip ties.
Slide pulling pliers are really useful. They grip around the slide ferrule, and then you tap with your hammer. This allows you to use some force on the slide without crushing the tube.
For woodwinds, being able to replace corks under keys, on clarinet tenons, and saxophone necks can be very useful. You need a supply of cork (good stuff, not corkboard quality stuff), sharp razor blades, contact cement, and some fine grain sandpaper or emery cloth. Most of this you can get at Michael's or a similar hobby store.
A leak light is also very useful. Don't get the cheap rope light junk, get a good one.
Past this level you start getting into really expensive dent tools...that's a whole other issue.