Over the summer, Spotify finally opened for business in the U.S. and included a free, ad-supported option in its offerings. Now both MOG and Rdio, two other subscription music services, are adding big free components themselves.

Tomorrow MOG is rolling out a Web-based, ad-supported version of the service that gives users an undisclosed amount of free streaming music, which they can keep listening to if they engage with the service in certain ways, like sharing playlists with friends.

And soon Rdio will offering something similar, with two differences: Its free version will be ad-free, and the company won’t prompt users to take certain actions to keep the free going. It will decide, out of the user’s sight, how long to extend the free trial period, with the intent of getting them to upgrade to a $10 monthly subscription.

The timing of the new free services aren’t accidental. They’re both being announced in advance of Facebook’s F8 developer conference next Thursday. That’s when the social network is expected to announce a new music service that will incorporate MOG and Rdio as well as Spotify.

Details about Facebook’s service are still sketchy, but the primary gist is that Facebook won’t be building its own music service. Instead it will work as a hub that allows existing services’ users to share their tunes with their friends.

But it’s very unlikely you’ll be able to listen to a friend’s Spotify song unless you’re a Spotify user yourself. So it’s crucial for the services to make sure that signing up to use them is as easy as possible. And requiring someone to pay to listen to a friend’s song seems like a non-starter.

Hence: Lots of free trials that last for an undefined period.

Rdio CEO Drew Larner won’t comment about Facebook and its upcoming service. But he will talk about the strategy of offering free music, but only for a limited time. “We know free is powerful, it’s a great way to increase your funnel,” he says. “But it’s about not creating a tier for an alternative or replacement for what would be a paying subscriber.”

Ultimately Rdio, MOG and Spotify, along with services like Rhapsody, are all trying to get to the same place. They want customers to pay them a $10 monthly fee for unlimited music that works on both the web and devices like Apple’s iPhone and Google’s Android.

That’s a model the music industry was never happy about until recently, in large part because free ad-supported services like iMeem, MySpace Music, Qtrax, and Spiralfrog sputtered and/or failed completely.

The other option for music fans who don’t want to pay for music but don’t want to break the law is to play with Web radio services like Pandora and Clear Channel’s new iheartradio.

Those services let you listen to unlimited music, for free, but don’t give you on-demand access. Instead, you need to let them program your music for you in some capacity.

Somewhere in between the two sits Turntable.fm, which is also free, but gives users more control of their music — for now, at least, while the company tries to hammer out label deals. The service is also expected to play a role in the F8 announcement next week.

Which is essentially what Qtrax, which claims to be the world’s first free and legal peer-to-peer music service, has done. Qtrax launched over the weekend with the alleged support of EMI, Universal, Warner and Sony. Today, all four labels are saying that while they have discussed relationships with Qtrax, they have not inked any formal agreements. “EMI Music had an initial agreement with QTrax, essentially a license designed to help them experiment with this ad-supported model,” an EMI spokeswoman told Wired. “QTrax didn’t launch the service during the period of the agreement–I think we initially did this two years ago. We’re now in talks with the company about a possible new deal, but as of today, they don’t have a license with EMI Music.”

A source inside Warner told the Times Online a similar story: “Warner Music Group has not authorized the use of our content on Qtrax’s recently announced service.”

Oh, but it will. Just you wait, says Qtrax CEO Alan Klepfisz, who admits that the “ink hadn’t dried” on some of the company’s claimed deals. “We are not idiots,” he told the Times Online.”We wouldn’t have launched the service in front of the whole music industry unless we had secured its backing. We feel we have been unfairly crucified because a competitor tried to damage us. Everyone is very upset. We do have industry agreements including the major labels. Even today we are working on more deals.”

Announcing the debut of Last.fm’s “unprecedented” on-demand music streaming platform, Jones–in a moment of Zuckerbergian grandiosity–proclaimed:

Today we’re redesigning the music economy.”

Which will no doubt come as a bit of a surprise to Apple, and Real, and Amazon and, above all, Imeem, which announced a similar ad-supported service last month.

To be fair, Last.fm’s free on-demand service seems a bit more compelling. Certainly, the CBS-owned site is the only one among the few to offer access to music from all four major labels and a host of independents to anyone willing to stare at an ad for while. And providing complete album streams on a “try before you buy” basis is truly a nice touch.

Still, Last.fm does have one significant limitation: You can listen to a track no more than three times unless you agree to pay for the subscription version of the service or purchase it from an affiliate. Will that be a deal-breaker for the average music fan or a good reason to buy your music through Last.fm, rather than iTunes? Hard to say. “The free-music-on-demand field has been a tough one, with many announcements but few real entries (consider, for example, the often-delayed Qtrax and vaporous Mashboxx),” notes the Los Angeles Times’s Jon Healey. “With CBS’ backing, Last.fm might be able to search longer for a workable formula than the typical start-up. But at some point, it has to find a way to pay the bills.”