Next, whose roots go back to Old English niehsta, has been an English adjective and adverb for centuries; it can also be a noun ("The next will be better"). The predicate form of next has become widespread since the launch and subsequent success of Chatroulette, "a website that pairs random strangers from around the world for webcam-based conversations" (Wikipedia).
Julia Ioffe profiles Chatroulette's founder, a Russian 18-year-old high-school dropout named Andrey Ternovsky, in a May 17, 2010, New Yorker article, "Roulette Russian." Here's how she explains Chatroulette and "to next":
The idea is simple. When you log on to Chatroulette.com, you see a sparse white window with two boxes. One box shows your own image, courtesy of your Webcam; the other is for the face of what the site calls, somewhat ambiguously, a “partner.” When Partner appears, you can stay and talk using your voice or your keyboard, or you can click “Next,” which whips you on to someone new. The point is to introduce you to people you’d never otherwise meet and will never see again—the dancing Korean girls, the leopard-printed Catman, the naked man in Gdansk.
More than a million people, most of them from the United States, clog Chatroulette’s servers daily. To “next” someone has become a common transitive verb. Catman is an Internet celebrity, as is Merton the improvising pianist. Brooklyn bars throw Chatroulette parties, an indie band has used the site to début an album, and the Texas attorney general has warned parents to keep their children far, far away.
Move on to the next woman. It's what intelligent and expirenced [sic] people tell idiotic newcomers to do, but they don't listen, and continue to pursue the same woman by giving her flowers and being nice and polite and showing good manners while she goes off and fucks some outlaw biker. Then she tells him about how good the outlaw biker was, and enventually [sic] she cries on his shoulder about how the outlaw biker treats her like shit. When and if he asks her out she tells him that she's sorry but she doesn't feel that way about him, and that she just wants to be friends.
God, I'm bitter.
"There's this girl.... blah blah blah.... and she actually looked at be... blah blah blah... I could tell she really liked me, because her eyes were open... blah blah blah blah"
"Dude, just next her, It's obvious she doesn't like you, and she just wants to fuck an outlaw biker. You screwed up, man. Just move on."
"No, I really think I'm in love this time, I'm mean she so pretty, and I think about her all the time... and blah blah blah blah"
And from August 2007:
verb, transitive: to discard someone and move on to the next person; often used in cyber-dating but also used in meatspace
Darlin', after what you did to me, I've got half a mind to next you, but I'll give you one more chance.
UPDATE #1: I wrote this post, and scheduled its publication, before I had the opportunity to read Wishydig's post on nexting. Wishydig writes: "One reason nexting became so common and so necessary was the ubiquitousness of self-gratification. Ten minutes on that site makes me want to seriously reconsider shaking any guy's hand again."
UPDATE #2: My own post on the origins of the Chatroulette name.
Image: Logo designed by Paul Rand for NeXT Software, Inc., a company founded by Steve Jobs in 1985 after his forced resignation from Apple. (Rand charged Jobs the then-extravagant fee of $100,000, many times more than what Rand had charged IBM for the latter company's logo.) The company originally made computers and the software that ran on them; it also created WebObjects, a web-development platform still used by Apple in its iTunes store. NeXT had limited commercial success and was sold to Apple in December 1996 for $429 million. Jobs returned to Apple in 1997.