Just like everyone else, most of my repairs involve replacing wear items (tubes, tires, derailleur and brake cables, brake pads, chains) and truing wheels.
All of these items require only cheap tools and/or tools all people should probably own, along with a decent bike pump.
In the spirit of trying to be helpful, I do know people who will fix flats and change tires, but are paranoid about replacing cables and chains and adjusting derailleurs/brakes on their own. I'm not sure what kind of tool might make that intuitive for more people; some people are just convinced that they are not mechanically inclined.