Microsoft XNA is composed of industry-leading software, services, resources, and communities focused on enabling game developers to be successful on Microsoft gaming platforms.
Reference: http://msdn2.microsoft.com/en-gb/xna/default.aspx
Free Game Engine for Xbox 360 from Microsoft
Yes, XNA Game Studio is very good, you do, though, need Visual C# installed to use it (minimum Visual C# 2005 Express Edition). I like making the games for XBox, even though I don't have an XBox
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