"Lummox" had a bit of a run, but there is a hint of stupidity in the word. The lummox is clumsy because thy're an unthinking animal. They are a beast who smashes things without knowing it. The lummox at least is afforded the dignity of being unaware. The klutz's wretchedness is compounded by awareness. The klutz knows they are a klutz, and hates themself for it. The klutz will always do their best not to be a klutz, and that will make things worse.
Nowadays, klutzes are everywhere. The Westerly Sun newspaper recently asked "Are you really a klutz in the kitchen?" The Janesville Gazette wrote of the Simpsons that "the father—Homer Simpson—is always an idiot, always a klutz, always the least intelligent character in any episode." CNBC titled a recent story "How a klutz like me saved $$$ doing DIY repairs."
For a word of such popularity, it was adopted relatively recently into the English language. If I had to guess the moment klutz entered the English language, I would guess it happened in 1968, and was the result of the publication of Leo Rosten's "The Joys of Yiddish." He included the word in his book, and the book was a bestseller and something of a national phenomenon. I suspect more than a few Yiddish words made the jump into the mainstream following the publication of Rosten's book; it's certainly the moment klutz starts making an appearance in the national press.
The earliest newspaper reference I find is from the syndicated column "Earl Wilson's New York" from February, 1970, which quoted actress Michele Lee as saying "I'm a klutz." The New York Times didn't use the word in an article until 1974, in a profile of actress Valerie Harper, who said ""I always felt like a klutz next to those other skinny girls, as we twirled our adorable little parasols."
I suspect the word's popularity has another source: There's Klutz Press out of Palo Alto, California, which publishes instructional books for the self-diagnosed klutz: "Juggling for the Complete Klutz," "The Klutz Book of Knots," and "The Klutz Book of Paper Airplanes." They began publishing in 1977, and I can't recall the last time I went into a bookstore without seeing their books prominently displayed. If a language is a dialect with an army and navy, as Max Weinreich said, then an idiom is just slang with a endcap at Barnes and Noble.
Here are some examples of the word klutz used in a sentence:
The Heebie-jeebies at CBGB's: A Secret History of Jewish Punk, Steven Lee Beeber: "They also let Handsome Dick [Richard Manitoba of the Dictators] gradually take over as lead singer, substituting his comic rants and drunken klutz antics with a guttural approach to singing and shouting at the audience."
Current Biography Yearbook, 1980, Volume 41: "One of the charter members of the Not Ready for Prime Time Players, the late-
Women who Love Sex, Gina Ogden: "He thought he was supposed to know how to do everything, and he felt like such a klutz. He was a klutz. But I loved him."