Like Draw Something and Words With Friends before it, SongPop is based on an old idea: in this case, it’s basically Name That Tune, a TV game show that ran in various incarnations from the early ’50s to the mid-’80s. Draw Something, of course, is based on the parlor game Pictionary and Words With Friends is essentially Scrabble on a slightly different board. In all three cases, there are no complicated rules and there are no steep learning curves — you just start playing. SongPop presents players with a set of four choices of song titles or artists: the music starts and players make their guesses as quickly as they can.

The game is a natural, and it probably would have been at least a middling success no matter what. But it got an extra boost after Mark Zuckerburg wrote on his Facebook (FB) page on June 21: “SongPop is one of the most fun Facebook games I’ve played in a while.”

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Usage “skyrocketed” after that post, says Mike Thompson, the lead writer for Inside Social Games. “We very rarely see a game take off like that.”

And the trend still seems to be up. As of Wednesday, SongPop had 18.1 million monthly active users on Facebook, and 4.2 million daily users, according to AppData. That’s up from 14.6 million and 3.4 million, respectively, on August 13. The game is also popular on both iOS (AAPL) and Android (GOOG) mobile platforms.

Nobody is as surprised by how quickly people have taken to the game as its co-creator Mathieu Nouzareth. He founded FreshPlanet, the company that owns SongPop, along with his brother Romain. “This is not the kind of success you can predict,” he says. “You can hope for it and dream about it, maybe.”

On the day of Zuckerberg’s post, “we saw the traffic jump within seconds,” he says. “We thought maybe we were under attack or there was a bug.” Almost as quickly, the phone lines were jammed and the resumes started flowing in.

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About two thirds of those playing via mobile devices log in through Facebook. The idea from the beginning, Nouzareth says, was to create a game that combines the strengths of social media and mobile technology. Many games are designed more for one platform than the other — for instance, Angry Birds is a huge mobile game that users play by themselves, while many of Zynga’s (ZNGA) most popular games, such as Farmville, are social and limited mainly to Facebook. “I expect that in the future, there will be a lot more games that combine the two,” Nouzareth says. And indeed, that combination is another thing that SongPop shares with other big successes like Draw Something and Words With Friends.

So far, the game isn’t profitable. “Costs are very, very high,” Nouzareth says, particularly server costs — “it’s insane how high they are.” But he says the break-even point should be reached within the next few months.

Revenue comes in the form of advertising, in-game purchases (for, among other things, access to more songs and more genres), and traffic the game sends to iTunes for music purchases. Nouzareth won’t say how big a cut the company gets from music sales, but called it a “tiny percentage.” He also declined to talk about total revenues.

Though SongPop is still gaining users, the growth rate has softened in recent weeks. There could be some natural barriers that will keep it from staying in the top ranks for the long term, like, say, Angry Birds. For one thing, not everybody has the same tastes in music, and few fans of modern country will want to play against aficionados of hip-hop. Users determine the genres, so they tend to pick the ones they know best — if your opponents’ tastes are markedly different, it will be less fun. So the game is somewhat limited to friends playing friends. Words With Friends, despite its title, is much more amenable to strangers playing each other.

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For another thing, the game mainly appeals to a large but nevertheless limited population: music nerds. There are lots of music fans out there, but how many of them feel they know their stuff well enough to quickly guess the identities of songs within a few notes? Enough for success, clearly, but maybe not enough for the game to become an all-time classic.

Even Nouzareth allows that the good times won’t last forever. “Games go up and down,” he says, and he’s already thinking about what FreshPlanet should do next. Still, SongPop is highly addictive, and it seems likely to maintain a healthy user base for some time to come. FreshPlanet employs about 15 people and for now “everyone is working on SongPop” he says.