I love flying (and miles) and don't really care about disconnects or missed connections. A good way to break up the flight if a long flight too. Ironically, I almost always choose no connections whenever possible due to intense ear pain during descent. One time it hurt so badly that I thought I was going to cry or that I lost my hearing -- had to see my doctor for it. I've been using airplanes during descent (works 90%) of the time, not foolproof but thank god for whomever invented them. So no talking to me during descent (because I can't hear that well) and that's why I never put myself in the emergency row (because during sudden descent, that'd be a huge problem).

So I avoid connecting flights like the plague only because of the pain. I'd also avoid it if it drags on my time to the destination too long (like if the connection is 4-5 hours long) but that's minor compared to my primary reason.