Which Version of Compact Edition doesn't need any additional installation on user machines-Collection of common programming errors

.NET 4.0 does not requires any previous .NET versions to be installed.

From SQL Compact 4.0 news blog:

Compact 4.0 CTP1 needs Visual C++ 2008 Runtime Libraries (x86, IA64 and x64), Service Pack 1: The native DLLs of SQL Server Compact 4.0 CTP1 need the Microsoft Visual C++ 2008 Runtime Libraries (x86, IA64 and x64), Service Pack 1. Installing the SQL Server Compact 4.0 CTP1 using the Windows Installer (.exe) file, also installs the Visual C++ 2008 Runtime Libraries SP1. If SQL Server Compact 4.0 CTP1 is deployed privately in the application’s folder the following have to be present on the machine for SQL Server Compact to function properly:

a.      Installing the .NET Framework 3.5 SP1 also installs the Visual C++ 2008 Runtime Libraries SP1.

b.      Visual C++ 2008 Runtime Libraries SP1 can be downloaded and installed from the location given below: http://go.microsoft.com/fwlink/?LinkId=194827

Note that installing .NET Framework 2.0 or 3.0 or 4 does not install the Visual C++ 2008 Runtime Libraries SP1.