While examples of the genre across the half-century or so of television are clearly fewer and farther between than demographically responsible, there's a clear trajectory that led to "Girls" (which notably features the youngest characters and frankest discussions of pretty much any of its predecessors).
From 1966's "That Girl" to a slew of shows that premiered earlier this season (including including the similarly titled "2 Broke Girls" and "New Girl"), here's a few examples:
That Girl (ABC, 1966-1971)
Though "The Mary Tyler Moore Show" deservedly gets a lot of credit as a pioneer of the professional single women television genre (let's face it, it was a much better show), "That Girl" was definitely its forerunner. The first sitcom ever to focus on a single woman (at least one who was not a maid or living with her parents) came in 1966 when Marlo Thomas brought the character of Ann Marie to airwaves. An aspiring actress who moves to New York City from her small hometown, Thomas based the premise of her own life trying to get into acting. Thomas herself was the real creator of the show (originally titling it "Miss Independence"), but she wasn't credited as such, explaining in retrospect that she "played down her power" purposely to not come across as threatening. Either way, her influence is clear. It was Thomas who fought to leave her character unmarried at the end of the show's five-year run, not wanting to send the message that that was the ultimate goal for young women.
The Mary Tyler Moore Show (CBS, 1970-1977)
Widely considered one of the greatest sitcoms of all time, "The Mary Tyler Moore Show" was clearly a huge influence on so many female-led sitcoms that would follow it (it's even name-checked 40 years later in "Girls"). Starring Moore as the iconic Mary Richards, the show ran for seven seasons in the 1970s, winning three consecutive Emmys for best comedy series. Richards' character was a thirtysomething, never-married, successful television producer who remained single throughout the show's duration (though had two somewhat serious relationships at times). And in addition to her, "Mary Tyler Moore" gave us a quartet of other classic female sitcom characters (though not all of them quite as independent as Richards) in Rhoda Morgenstern (Valerie Harper, who who would spin-off the character in "Rhoda), Phyllis Lindstrom (Cloris Leachman), Sue Ann Nivens (Betty White) and Georgette Franklin (Georgia Engel).