Rest assured that XNA Framework games will run on Windows XP and Vista as long as you have the correct dependencies installed and all your content in the right place. Its VERY unlikely to be a bug so please check everything very carefully before asking.

For games built with the 1.0 XNA Framework:

1. .NET Framework 2.0 - included as an OS component on Vista so not required to install there.
2. DirectX 9.0c *See note below
3. XNA Framework Redistributable 1.0

For games built with the 2.0 XNA Framework:

1. .NET Framework 2.0 PLUS the C++ 2005 SP1 Redist -OR- .NET Framework 2.0 SP1
   Some notes on these dependencies:
   • The .NET Framework 2.0 is included as an OS component on Windows Vista, Windows Server 2008 and Windows 7, so you only need the C++ Redist for these operating systems
   • The standalone .NET Framework 2.0 SP1 installer will not run on Windows Vista - you must install 2.0 SP1 bits by installing either Vista SP1 or the .NET Framework 3.5
   • You may have either of these 2 already installed by other applications on your system (such as Visual Studio 2005 SP1 or the Games For Windows - LIVE Redistributable), but don't rely on them already being installed if you are writing an installer.
2. DirectX 9.0c *See note below
3. XNA Framework Redistributable 2.0
4. Games that create a GamerServicesComponent/use live networking REQUIRE a full XNA Game Studio 2.0 install.  The Games for Windows - LIVE Redistributable is NOT sufficient since there are non-redistributable components in XNA Game Studio 2.0 that are required.  This will also satisfy the VC++ 2005 SP1 redist requirement, you don't need both.

For Games Built with 3.0 XNA Framework:

1. .NET Framework 2.0 or .NET Framework 3.5, depending on whether or not your game uses .NET 3.5 features.  Note that the .NET Framework 2.0 is included as an OS component on Windows Vista and Windows Server 2008, and the .NET Framework 3.5 is included as an OS component on Windows 7.
2. XNA Framework Redistributable 3.0 - the C++ redist and the relevant DirectX components are included in the XNA Framework Redistributable 3.0 and do not need to be installed separately anymore.
3. Games that create a GamerServicesComponent/use live networking REQUIRE a full XNA Game Studio 3.0 install (see this thread).  The Games for Windows - LIVE Redistributable is NOT sufficient since there are non-redistributable components in XNA Game Studio 3.0 that are required.

For Games Built with 3.1 XNA Framework:

1. .NET Framework 2.0 or .NET Framework 3.5, depending on whether or not your game uses .NET 3.5 features.  Note that the .NET Framework 2.0 is included as an OS component on Windows Vista and Windows Server 2008, and the .NET Framework 3.5 is included as an OS component on Windows 7.
2. XNA Framework Redistributable 3.1 - the C++ redist and the relevant DirectX components are included in the XNA Framework Redistributable 3.1 and do not need to be installed separately anymore.
3. Games that create a GamerServicesComponent/use live networking REQUIRE a full XNA Game Studio 3.1 install (see this thread).  The Games for Windows - LIVE Redistributable is NOT sufficient since there are non-redistributable components in XNA Game Studio 3.0 that are required.

You do NOT need to install Visual C# Express, Visual Studio or XNA Game Studio unless you require any of the following:

• 2.0, 3.0 or 3.1 games using GamerServices or Microsoft.Xna.Framework.Net.*
• XnaPack utility to create and/or deploy .ccgame packages
• Runtime usage of content pipeline creation components (such as in the WinForms samples)

*DirectX note: Don't assume you already have it even if other games run - there are optional parts which may not be on your computer. Run the web installer and it will check and add missing parts. Don't assume that because you have the latest SDK installed that it will work either as SDKs do not install the optional files from previous SDKs.  We can not stress this point enough - its the most common reason for XNA apps failing and we often see people who ignore this step becuase they think they know better.

If the application still doesn't run after installing the components listed above, then check the following:

1. Follow the advice in this thread - you may find the exception is happening in your code.
2. Try some of the samples - if they run then the problem is in your code. Start with the empty Game template as it uses no content and has the minimal set of dependencies.
3. Check out Process Monitor (formerly FileMon) - this will help you identify if you have missing DLLs, missing content or content in the wrong place.