NEW YORK (Reuters) - The future of the music business is social, free -- and hopefully profitable.

After a decade when sales tumbled 50 percent, record labels cut thousands of jobs and more than 35,000 consumers got sued for illegal downloads, the industry is coming around to the idea of giving away songs as a way to get customers to pay.

This week MOG and Rdio became the latest U.S. digital music startups to offer online streaming access to millions of songs for free, hoping that the slick user-friendly interfaces and deep libraries will convince users to become paying monthly subscribers.

They follow London-based Spotify, whose 18-month-old streaming music service has taken Europe by a storm. After numerous delays, it entered the U.S. market in July.

Other digital services with free access to music will emerge in coming months. Beyond Oblivion, a start-up with backing from News Corp, plans the Boinc service, which will take a different approach by enabling free access to music for users who buy special devices.

The key to success for these services -- and by extension the record labels -- is the conversion rate to paid from free. Spotify has said it has more than 10 million registered users with 1 million now-paying subscribers, for a conversation rate of 10 percent.

Music streaming services typically charge $5 to $15 a month to play any song or album the user wants from a library of songs via computers and mobile devices.

The free/subscription trend comes as sales of downloaded songs have begun to slow down at Apple Inc's iTunes, the No. 1 music retailer by far.

MOG and Rdio announced their new free features just ahead of Facebook's developers' conference next week in San Francisco, where sources have said the No. 1 social networking website will launch a music platform.

Those two companies, along with Rhapsody and Rootmusic, are expected to be a part of the launch, which is designed to make it easier to share music and hopefully win paying subscribers from Facebook's 750 million users.

MOG's free service gives users more songs as they engage other users, particularly if they log on using Facebook's Connect platform.

"It allows us to reward the tastemakers and influencers," said MOG Chief Executive Officer David Hyman, a former senior MTV executive.

Nervous about appearing to encourage the idea that music should be free, music executives privately argue these services are more limited than they initially appear.

"It's not a shift to free," said a label executive who requested anonymity because negotiations with the services were private. "We're building a larger funnel and driving more consumers to a subscription service."

USERS AREN'T BUYING

Typically, the free portion of these services feature advertising, but revenue from that does not yet cover the licensing fees that major labels charge.

But Rdio is going a different route. It will not feature advertising and, unlike MOG, will not manage free music based on users' engagement.

"We won't ask users to spam their friends," said Chief Operating Officer Carter Adamson. He added, however, that user engagement data will determine the number of songs a given user can access on its free platform.

The company's founders, Janus Friis and Niklas Zennstrom, invented one-time music industry file-sharing nemesis Kazaa and communications service Skype.

So far, subscription music services have struggled to capture the collective imagination of everyday music fans. Industry sources estimate MOG and Rdio each have fewer than 100,000 subscribers.

Rhapsody, the biggest U.S. music subscription service, has been in business for 10 years and only has a paltry 800,000 subscribers, according to its last publicly stated numbers.

This week the company added a new social focus that makes it easier for users to follow each other and share music within the Rhapsody community and around the Web.

Rhapsody spokeswoman Jaimee Steele said the company would consider an advertising-supported service if the economics made sense, but added that there has been little evidence of that to date.

While free might appeal to users, it can be expensive for start-ups that could easily burn through all their funding by paying labels' licensing fees.

"We have no intention of going out of business in six months," Rdio's Adamson said, emphasizing that the company will be careful not to give away free music to "serial abusers."

"All of these services have VCs, investors and boards -- all of whom expect some sort of return on their investments," said a second record executive who isn't permitted to publicly discuss private negotiations. "As a result, limited free tiers are being offered to get people in the doors. The emphasis is on 'limited.'"

Meanwhile, major labels are starting to share the risk from innovative business models after years of suing grandmothers and children for illegal downloading, shutting down game-changing start-ups like Napster and demanding hefty upfront fees from entrepreneurs who tried to work with them.

Label executives are eager for music fans to sign up for subscription services, if only because these businesses promise steady guaranteed revenues similar to the cable television industry.

(Reporting by Yinka Adegoke; Editing by Peter Lauria and Lisa Von Ahn)