Stuff like this terrifies me, especially when I'm doing something that I really do need to get deep under the car.
I've also had a few "reality checks" when jacking that made hyper aware. The first was jacking my MG by the rear differential(live axle, so a safe practice generally) and having the differential slip off the jack. The second was jacking my Lincoln in my parents driveway, which has a subtle but pesky slope that I had forgotten about. I shouldn't jack anything on it, but in this particular case I hadn't set the parking brake. Almost as soon as the front wheel was off the ground, it rolled backwards and killed a 2 ton compact trolley jack in the process(bent it sideways).
My practice for a while has been to raise the car, set it down on the jackstands, and then raise the jack back up so that the saddle is touching the jacking but not bearing any weight if that makes any sense. My thought on that is that if the stand should fail, hopefully the jack will catch it enough for me to remedy the situation. Of course I also do tires under the car, etc. On the MG, though, there's a limit to how much I can do as it's not very long and I need to get myself under there too.
I keep a couple of different sizes of jackstands on hand. The little 2 ton ones are handy if I'm not lifting very high, and sometimes a 3 ton at its lowest height is too tall. The 2 tons feel too rickety to me if raised more than a couple of clicks. My 3 tons use pins, which are less convenient but also feel sturdier to me.