2 days ago Epic released Unreal Development Kit (UDK), a free (for non-commercial and educational use) edition of the Unreal Engine 3 (UE3). Here's the official announcement. There's also an official forum where I already found a solution with some installation issues.
This is definetely something I'm gonna at least experiment with and maybe even try to use it to create a simple game, which hopefully doesn't end up in my plethora of barely started and never finished games using various tools lying around my computer.
What I learned from the forum is that if install fails with a problem with Visual Studio 2008 redistributables and you already have them, just add -SkipNETCheck parameter.
Here's a Unreal Development Diary video about a game rapidly created by a single person which shows what you can actually do with the engine: