The answer would depend on your definition of “the simplest”…
Warrior is the simplest to understand for a newer player. Prot was my first tank spec ever, and, even as a complete newcomer, I was still doing on it reasonably well. Almost all their abilities are very straight-forward and easy to grasp. I mean, “Shield Wall”, “Shield Block”, all that. The might not be able to finish pulls and bosses when they are the last man standing, though.
DH is the simplest if you struggle with button management. I main this class now, and it has by far the lowest amount of abilities to put on your bars. But! There’re non-obvious intricacies of how you use them, these abilities, which you wouldn’t probably pick up yourself without a guide. They are probably the best one to deal with Tyrannical, though.
Druid is currently the simplest if you want to, well, get into groups and play the game. And that’s for a good reason, because, with today’s tuning, they are reliable, effective, and self-sufficient. You can survive the craziest pulls on Druid, do massive AoE, help your healer, and bring dead Hunters back to life (to die again).
Paladin is the simplest to achieve results, I mean to actually time your keys. Because this class can handle most of dungeon mechanics all by itself, so you would do amazingly well in less-than-optimal group compositions. Paladins have started to fall behind a little in numbers, but they’re still in a great spot and loved by healers.
As for Monks and DKs, I could also come up with a field where they would be the simplest (doing damage and with sheer survival capabilities), but that would be a disservice. Because these two last classes aren’t simple to play (or to understand from the get-go) in any sense.