Rhapsody established itself as the first important paid music service a decade ago, after Napster and a worldwide binge of illegal file sharing spooked the music industry. But now it is being outshined by Spotify, a European-based rival with a similar business model. It was Spotify, not Rhapsody, at center stage last week at Facebook’s f8 developer’s conference in San Francisco. Spotify CEO Daniel Eck was Mark Zuckerberg’s first guest during the widely watched keynote. After the two touted a slew of new social music features, Zuckerberg flashed a slide featuring other online music partners, Rhapsody included. It appeared so briefly it could have been an afterthought.

The slight comes amid continued change for the music industry. Earlier this year, Nielsen (NLSN) SoundScan reported that overall U.S. music sales were down 2.4% in 2010. Digital sales were up, however, and subscription-based services appear poised for growth. Research firm ABI projects that by 2016 some 161 million subscribers will be accessing music from their mobile phones around the world, up from just 5.9 million this year. Online subscriptions revenues were about $201 million in 2010, according to the Record Industry Association of America. Despite a ten-year head start in that very business, Rhapsody suddenly finds itself trying desperately to catch up to the momentum of a glitzy newcomer. What happened?

Rhapsody may simply have been ahead of its time. It advocated storing music in the cloud long before the idea, let alone the term, was in vogue. The result, according to Paul Resnikoff, founder of the Southern California-based Digital Music News, was often clunky and confusing. The company also underwent multiple convoluted transformations. In 2004, it was acquired by RealNetworks (RNWKD) and spun off again three years later as a joint venture with Viacom (VIA). Last April, it rebranded itself as Rhapsody International.

The company is private and does not release its financial numbers, but it says it has some 800,000 subscribers paying $10 a month. Rival Spotify has 1.4 million U.S. users, about 170,000 of which pay either $4.99 or $9.99 a month, according to a source cited by Billboard.

Rhapsody hasn’t taken Spotify’s ascendency lying down. On the fringes of Facebook’s conference, it revealed a new 30-day free trial membership offer and, with it, a new strategy: an emphasis on mobile. Its app gives users access to the company’s 13 million songs and, as we sit in a San Francisco café, president Jon Irwin sifts through music on his phone with a palpable excitement. He opens up a number of albums and playlists, including “19” by Adele and “Chicksongs,” a user-created playlist consisting entirely of songs whose titles are a female name. Users consume 30% more music on mobile devices than on desktops, he notes.

Irwin has never been a fan of the so-called “freemium” business model. But he admits that Rhapsody’s free trial is exactly that: a taste of the product with certain restrictions — in this case, a time limit. He stresses that it is different from competitors’ offers. By comparison, Spotify’s free version is ad supported, restricted to desktop usage and caps the number of song plays after six months. Rhapsody has tried the tactic before, offering two-week and 60-day free trials. Both required users to submit credit card information, deterring many from signing up.

It’s not yet clear how Facebook will impact the company either. Its 800 million active users will soon be able to post what songs they are currently listening to while friends will be able to listen instantly via partnering music services. That could provide a huge swell of traffic, but also sharpen competition. Irwin believes smaller providers, such as Mixcloud and Rdio, will eventually fall to the wayside in the battle for Facebook’s users. Irwin thinks the scheme will favor the services with the most existing customers, helping Rhapsody. “One advantage that we have right out of the gate is that, in the on demand music business, Rhapsody is by far the largest,” he says.

Indeed, Rhapsody has been a success with diehard music fans and could find itself with a legion of devoted listeners sharing music on Facebook. According to the NPD group, Rhapsody users spend the most money on physical CDs and digital downloads. “It’s really for the hardcore music user,” says Russ Crupnick, a consumer and retail market researcher with NPD. Hooking casual fans may be harder. “The problem is trying to turn their 800,000 subscribers to 8 million,” he adds.

It’s clear that Spotify is a formidable foe. It’s raised millions from prominent investors including Silicon Valley’s Kleiner Perkins. And it’s got the hype and momentum consumer product makers crave. That could change, of course. More likely is that the two services continue to battle it out. Now that its model has been widely accepted, Rhapsody has to find a way to deal with tough competitors that have adopted it too.