What is proper way to wire hard wired LED strip light power supply/controller/driver?
I'm pretty sure the proper way involves using a (large) electrical box (Thanks Nate S).  They make them in a variety of sizes--some quite large, like the ones holding your circuit breakers.  I saw a picture of a large one containing a large switching power supply.  You mount it some place out of the way, like in the basement, or in the attic (if you have access) and then run low voltage wires to the room/led tape.

If the power supply is pigtailed, I also think you could butt it up against an electrical box and have the high voltage wires enter where it butts up.  That way no high voltage wires are exposed--kind of how I see the doorbell or boiler transformer mounted to a box.  I'm basing this solely on the transformers I've seen.