What does the free edition of Starcraft 2 include?

This info is outdated. Here's the answer for anyone interested in getting SC2:

You are not restricted to 4 maps or to terran only: You have full access to all races, maps and mods in "custom game", and all games in the arcade.

However, you still cannot play ranked ladder games and you can only play against easiest or easier AI in single player scenarios (though you can get around this by starting a "co-op vs AI" multiplayer game, setting the game's difficulty higher, adding an AI and playing against them).

You are also still restricted to the first 5 missions of the Terran campaign, and only the first two Terran challenge missions.

You also cannot test or publish your own maps, though you can make them.

Your level is capped at 15 (5 for each race), preventing you from unlocking any skins and most decals (though these aren't important features).

Some of the features:

• The first four missions of the StarCraft II: Wings of Liberty single-player campaign, including Mar Sara 1-3 and the choice to
  embark on Tychus’s first mission or Dr. Hansen’s first mission.
• The first two Challenges: Tactical Command and Covert Ops.
• Access to the terran race in Custom Games and Single-Player vs. AI.
• Access to the following custom maps (map selection may rotate over time):
  • Xel’Naga Caverns
  • Shattered Temple
  • Discord IV
  • High Orbit

And some of the restrictions:

Q. What are the restrictions of StarCraft II: Starter Edition?

A. Starter Edition players can only play up to the fourth campaign mission, and most Challenge Missions are unavailable. Starter Edition players are also unable to use versus and co-op matchmaking, most custom maps, chat channels, and the party system. Publishing custom maps to Battle.net is also restricted, and offline play is unavailable to Starter Edition players. For single-player and custom games, Starter Edition players may only choose the Terran race.

You can find this information and more here.

This means you can not play ranked games, but you can play vs your friends in the 4 maps that are available for starter edition but only as Terran.

There is an exception if your friends own Heart of the Swarm, which includes a Spawning feature. You may party with any Heart of the Swarm friend to temporarily upgrade your Starter Edition to a Spawned Edition of the game. While spawned, you may play any multiplayer game type and map with them, including ranked games. As a starter player, your race will still be locked to Terran. When you leave the party, you will be downgraded back to Starter Edition.