I don't have great stuff, but I've been able to do a lot with it.
A standard Radio Shack 2-setting soldering iron. 15W / 30W I think.
A pretty standard digital multimeter - if you don't have one get one with continuity buzzer.
A self-powered desoldering tool (heated tip) with the red-rubber bulb on it. If I lost this I'd buy another right away as it works great for me for all but the very fine components. I've never had luck with desoldering braid or the pumps that are spring loaded.
A TekTronics oscilloscope from the 1970s. I was given this for free and have to learn how to use it - might even need to be calibrated.
I also just ordered a logic probe which I will need to learn how to use.
I've been soldering for years now so am pretty comfortable/good at that. Just need to advance my knowledge with the scope and probe. Basically, I'm at the stage where I can replace components if it is obvious which ones are broken (i.e. burned components, dead LEDs) or someone tells me what needs replacing, but I don't know how to diagnose problems within a circuit path that are not obvious.
I'm fine with low voltage stuff (i.e. vintage computer circuit board) but working around anything AC or inside a CRT scares the pants off me (which is probably a healthy disposition).