The European online music service Spotify offers six million tracks—a practically limitless catalog spanning Aaron Copland to ZZ Top—in an interface as polished and intuitive as Apple’s iTunes. And unlike the pay-per-song iTunes, Spotify’s entire library is free for the taking, assuming users can tolerate an occasional advertisement.

The service is presently confined to Europe, where it’s available in the U.K., France, Spain, Norway and Sweden—but it is planning a U.S. launch for early 2010. The prospect is surely creating a little anxiety at Apple’s Cupertino, California, headquarters.

Inside the tech world, the summer days have been flush with news of Spotify’s rise. Facebook CEO Mark Zuckerberg proclaimed Spotify “so good” amid chatter that the two companies have been secretly negotiating a partnership. The Hong Kong billionaire Li Ka-shing confirmed that he had invested an undisclosed sum in the startup. And if back-of-the-envelope math is to be believed, Spotify is now valued at €170 million, or about $244 million.

When Spotify arrives in the U.S., Apple may find it difficult to compete with “free.”

In Europe, Spotify has shown itself a keen competitor. In August, the head of Universal Music in Sweden said Spotify has become the label’s largest source of online revenue in the country, overtaking iTunes. Now Spotify is turning its sights to the U.S., where a spokeswoman says the company plans to launch in “early 2010.”

So when the service crosses the Atlantic, will it unseat iTunes, or is it destined for the graveyard, like so many other ambitious music startups before it?

Test-driving Spotify turns even the most hardened cynic into a believer. Like iTunes, Spotify downloads onto a PC or Mac, offers access to a vast library of music (more than six million tracks, compared to Apple’s 10 million), and enables users to organize songs into playlists. The crucial difference, of course, is that with iTunes, songs must be purchased and stored on a computer’s hard drive, while with Spotify all the songs are free and stream instantly over the Internet. It’s not difficult to understand why bloggers have called Spotify “the best desktop music player we’ve ever used.”

In exchange for bathing in Spotify’s sea of music, users listen to short advertisements that play once every half-hour. For about $15 a month, depending on the country, users also may upgrade to a premium service that removes the ads and plays higher-quality audio. A subscription also allows consumers to use Spotify on a smartphone; otherwise, it’s not possible to access the music on the go, somewhat diminishing Spotify’s appeal. (A forthcoming iPhone app allows users to play Spotify playlists even without Internet access. Following speculation that Apple would reject the app, the iPhone maker last week approved Spotify for listing in the App Store.)

The fine print of Spotify’s agreements with the major record labels is unknown, but the startup presumably has to pay them royalties each time their music is streamed. (The labels own a substantial stake in the company, which some commentators have speculated amounts to an advance on those royalties.)

But one digital music entrepreneur says he believes Spotify’s revenue from advertising and premium subscriptions can’t possibly foot such a hefty bill. “There’s just no way to make any money,” says Michael Robertson, who founded MP3.com and is chief executive of the music startup MP3tunes. “Any time you have to pay a per-stream fee, the economics don’t work out for an advertising model...They’re going to go bankrupt, like all the other streaming companies as well.”

Those licensing fees will only increase once Spotify expands into the U.S., where iTunes today accounts for a quarter of all music sold—a larger share than Wal-Mart. The extraordinary growth of the iTunes Store over six years has been built on the premise that consumers are willing to pay for legal music online but don’t want to shell out a monthly fee to stream an unlimited amount of songs. “The subscription model has failed so far,” Apple’s Steve Jobs has said. “People want to own their music.”

When Spotify arrives in the U.S., however, Apple may find it difficult to compete with “free.” And the music labels, long suspicious of Apple’s dominance, may well greet the startup with open arms.

Nicholas Ciarelli is an assistant product manager at The Daily Beast.