I'm nowhere near as experienced as many of the posters that have already given their lists. I have seen or experienced a few events, though and found that most of the time they are trivially easy to deal with in a Rec environment.
I have had the following:
1) Overflow/dump valve fail on BCD (I had modified an old horse collar and this was my second dive with it.) No big deal, dive with very little or no air in my BCD anyway. Took it home and repaired the valve.
2) Minor freeflows due to cold water. Not full on freeze-ups but some 5 second freeflows here and there. (I've witnessed these, not had them happen to me personally.)
3) O-ring blown on a tank valve at the surface. No big deal, back on the boat, swap tanks and get wet.
4) A couple of minor second stage leaks and a minor first stage leak. Dribbling bubbles isn't a big deal, in my opinion. Watch the pressure gauge and repair during SI.
I keep my dive profiles conservative (as if I had a choice--still an air hog) and know how to service/repair my own gear. That, pre-dive inspections, and keeping a calm demeanor makes all of these equipment malfunctions non-issues.
You don't have to have massive amounts of experience to have a major failure. I've seen students in the pool who weren't even certified who had problems that would have scared the bejezus out of a lot of experienced divers.
The chances that something spectacular will happen obviously increases the more you dive, but it remains a lottery.
R..