Nebbish is primarily a noun referring to a weak-willed or feckless person, usually male and especially one who is socially inept and lacks self-confidence. The –ish ending makes the word sound like an adjective, though, so the word is also occasionally used in corresponding adjectival senses—that is, to mean weak-willed, socially inept, etc. Nebbishy sometimes fills this role.
Descended from the Yiddish nebekh, the word has taken several forms in its century or so in English, including nebesh, nebbich, and nebich, but the now-standard spelling was settled by 1960. In Yiddish, it was commonly used as an interjection expressing pity (e.g., “Nebbesh, those poor kittens!”), and a few such instances can be found in early use of the word in English, but in 21st-century English it is usually a noun or, less often, an adjective.
Due to its Yiddish origins, the word is especially associated with nebbishy Jewish people. On the web, it seems Woody Allen and George Costanza (from Seinfeld—the character is not Jewish) are the two examples most commonly cited in discussions of the word. Allen is especially dogged by it; in historical Google Books searches covering the 1970s through the present, a decent percentage of all instances of nebbish are associated with him.
You’d think a famous celebrity was coming, or an important client, instead of a nebbish little soap salesman from Nowhere, Ohio. [What’s the Big Hurry?, James Yaffe (1954)]
His physical atributes, and his quality of painful, halting honesty are usually at the mercy of some mediocre playwright’s effort to justify the bankruptcy of the American male, e.g., the nebbish with whom he so gallantly struggles in Two for the Seesaw.[Negro Digest (1966)]
Allen has taken a major step in his own characterization, making the transition from nebbish to nice guy. [New York Magazine (1973)]
Kissinger behaves like a pompous ass, and the Nixons come off as a couple of slightly befuddled, if well-meaning, middle-class nebbishes. [New Yorker (1987)]
Of course Portlanders fell for the quirky, late-night pizzeria like a nebbish male lead playing opposite Zooey Deschanel. [Willamette Week]
In a popular cartoon, two nebbishes slumped inertly in their chairs, feet outstretched on the coffee table, are saying “One of these days we’ve just got to get organized.” [Basic Social Policy and Planning, Hobart A. Burch]
Incredibly, he has gone from wisecracking windbag to fumfering nebbish, one with no answers. [New York Daily News]
We’ve all seen nebbishy-looking rich guys squiring unbelievably hot babes while the much better-looking waiters, doormen, and busboys burn with envy. [Waiter Rant, Steve Dublanica]