Multimeter or at least a test light.It's a safety thing first (make sure there's no live current in a wire) and it allows the repair of SO many things for next to nothing (like dryers). Before youtube, it could be daunting but you can watch a video on how to properly test just about anything.
I like the idea, but honestly, I think you guys are overestimating the average person's DIY abilities. This is a list for everyone, right? I know quite a few people (engineers and engineering students even!) who wouldn't even know what kind of oil to put into their car, much less where it comes out (this is why quick change places are so popular). I don't even own a hammer drill, and I do quite a lot of home and auto maintenance. and a Steam cleaner for windows? what ever happened to Windex and a paper towel?
Whatever you need, buy a cheap one first time round. If you use it lots or break it, buy a good one to replace it. If you don't use it, you've not lost much.