Look at HKLM\SOFTWARE\Microsoft\NET Framework Setup\NDP\v3.5\. One of these must be true:
The Version value in that key should be 3.5.30729.01
Or the SP value in the same key should be 1
In C# (taken from the first comment), you could do something along these lines:
const string name = @"SOFTWARE\Microsoft\NET Framework Setup\NDP\v3.5";
RegistryKey subKey = Registry.LocalMachine.OpenSubKey(name);
var version = subKey.GetValue("Version").ToString();
var servicePack = subKey.GetValue("SP").ToString();
Take a look at this article which shows the registry keys you need to look for and provides a .NET library that will do this for you.
First, you should to determine if .NET 3.5 is installed by looking at HKLM\Software\Microsoft\NET Framework Setup\NDP\v3.5\Install, which is a DWORD value. If that value is present and set to 1, then that version of the Framework is installed.
Look at HKLM\Software\Microsoft\NET Framework Setup\NDP\v3.5\SP, which is a DWORD value which indicates the Service Pack level (where 0 is no service pack).
To be correct about things, you really need to ensure that .NET Fx 2.0 and .NET Fx 3.0 are installed first and then check to see if .NET 3.5 is installed. If all three are true, then you can check for the service pack level.
I came to this page while trying to figure out how to detect the framework versions installed on a server without access to remote desktop or registry, so Danny V's answer worked for me.