Blizzard Entertainment announced today they have retired their demo of StarCraft II: Wings Of Liberty and replaced it with the Starter Edition. Players will get access to the first four missions of StarCraft II up to the point you either hit Tychus's first mission or Dr. Hansen's first mission. There will also be two challenges (Tactical Command, Covert Ops) and access to four custom maps (Xel'Naga Caverns, Shattered Temple, Discord IV, High Orbit.)
However unlike the original demo, StarCraft II: Starter Edition will require a Battle.net account and an Internet connection. Any progress and achievements through the first four campaign missions in the Starter Edition carries over to the full game should you wish to upgrade.
All the details are on the official Blizzard website if you are still thinking about trying the game. Apparently people like you still exist.