It really depends on what you want to do, some big ones are:
Unity: http://unity3d.com
They got a free trial version that you could use, it's really easy to start out with. The coding is done with C#, JavaScript or Boo.
Unreal Development Kit (UDK): udk.com/
Not something i would recommend if you're a beginner, quite difficult to get started with. The coding is done in form of scripting with UnrealScript.
While not really engines, you could always check out DirectX( http://www.microsoft.com/download/en/details.aspx?displaylang=en&id=6812 )/OpenGL(glut: http://user.xmission.com/~nate/glut.html ), coding are done in C++.
Again, not really an engine, but you can check out XNA( http://create.msdn.com/en-US/ ) for C#, really easy getting started with and you can run your games on xbox360 and windows phone 7.
Good Luck!