All valid concerns so far. However, the critical control case for single engine aircraft is crosswind landings. Unless you're in the aerobatic category, there's no requirement to recover from a spin.
But the driving factor for most H-tails (or E-tail in the case of the Connie) is simply reduction in overall aircraft height. Now that hangars that will accommodate 737s and larger are pretty common, you don't see multiple verticals all that often on modern designs. And the the exceptions that do pop up are usually Navy aircraft that have to fit below a carrier deck (F-18, E-2, V-22).
The only oddballs I can come up with are the F-15, F-22, MiG-29, and SU-27. I think in these cases, the amount of power involved means that an enormous tail would be needed in case of an engine out on takeoff. Therefore, it might actually be lighter to use twin tails since the bending moment on a single one would be extemely high.
Oh yeah, and then there's the A-10. The reason for the H-tail there is actually to help reduce the IR signature from the ground. So you can see, there's a variety of reasons why you might go that route. But in general, the fewer tailfeathers you have, the lighter the aircraft and lower the drag. That's the theory behind the V-tail at least.