|I find your lack of faith . . . disturbing.|
This is just a quick discussion on why some audiences really enjoy Klingons. There are a lot of quotation marks on words and phrases in this one—more than I "usually" use—because at the heart, Klingons tap into a bit of myth that isn't necessarily based in reality. We'll get to that toward the end, but it seemed appropriate to mention at the beginning so that the author's intent was a little more clear.
Klingons tap into a lot of things that audiences like, and like to see expressed. They are, fundamentally, another version of the “noble savage” myth—an idealized version of an individual—a warrior—born out of a “race” of individual warriors, who has the ability to indict our “civilization's” rules and speaks a kind of brute-force justice, but never steps over the line to unjust brutality such as against children or the weak. It's always been a sarcastic term, as there's no such thing as a “noble savage” society which is intrinsically better than any other, but we love the idea that our natural state has been corrupted (by whatever institutions) and that we can learn a “better way” from those who stand outside of it.
What's great about the Klingons, especially as TNG and DS9 explored them, is that their society is actually no less corrupt. It was politics, and not justice, that forced Worf's father, Mog, to make the decision to take on dishonor, while the House of Duras was allowed to flourish. Kahless, the Unforgettable, “returns” as part of a plot conceived by the priests of the Boreth Temple to rally the Klingon people back to their faith.
One of my favorite episodes is “Children of Time” which presented a future “colony” based on the crews' decedents, including those of Worf. Obviously, Klingon DNA was in short supply, but the “Klingons” were embodied as a philosophy, rather than a genetic heritage—the idea being that Klingons offer an ideal to aspire to, which is something we quite enjoy viewing, exploring and discussing.