<p>From within my Java program I want to determine which .NET Framework is installed on the system. What is the best (and easiest) way to do this?</p>

<p><strong>Answer</strong> Thanks scubabbl! It worked to check the directory <code>System.getenv( "WINDIR" ) + "\\Microsoft.NET\\Framework"</code> for its directories starting with the letter "v".</p>

From what I understand, the actual file structure in c:\windows\Microsoft.Net\Framework has folders with versions of .Net installed. On my computer, I have folders up to v3.5, or 
c:\windows\Microsoft.Net\Framework\v3.5.
There are lots of issues with this, including security issues though.
The second, and probably better answer would be to check the windows registry.
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\NET Framework Setup\NDP
The Version key will have the value you are looking for.
Edit: stackoverflow question regarding reading the registry with java.
read/write to Windows Registry using Java
This library
http://www.trustice.com/java/jnireg/
will allow you to read the registry.