I\'m making a network game (1v1) where in-game its p2p - no need for a game server.
However, for players to be able to \"find each other\", without the need to coordinat
Rather than a full-blown dedicated server, you could just get a cheap shared hosting service and have the application interface with a PHP page, which in turn interfaces with a MySQL database backend.
For example, Lunarpages has a $3/month starter package that includes 5gb of space and 50gb of bandwidth. For something this simple, that's all you should need.
Then you just have your application poll the web page for the list of games, and submit a POST request in order to add their own game to the list.
Of course, this method requires learning PHP and MySQL if you don't already know them. And if you do it right, you can have the PHP page enter a sort of infinite loop to keep the connection open and just feed updates to the client, rather than polling the page every few seconds and wasting a lot of bandwidth. That's way outside the scope of this answer though.
Oh, and if you're looking for something absolutely free, search for a free PHP host. Those exist too! Even with an ad-supported host, your app could just grab the page and ignore the ads when you parse the list of games. I know that T35 used to be one of my favorites because their free plan doesn't track space or bandwidth (it limits the per-file size, to eliminate their service being used as a media share, but it shouldn't be a problem for PHP files). But of course, I think in the long run you'll be better off going with a paid host.
Edit: T35 also says "Free hosting allows 1 domain to be hosted, while paid offers unlimited domain hosting." So you can even just pay for a domain name and link it to them! I think in the short term, that's your best (cheapest) bet. Of course, this is all assuming you either know or are willing to learn PHP in order to make this happen. :)