.NET is a programming framework similar to Java. To run programs made with .NET, you need .NET runtime, just like is the case with Java.
.NET versions however are not backwards compatible, each of them is like its own isolated framework. Which means you need 1.x to run programs made with .NET 1.x and so on. Currently there are three major revisions of .NET, 1.1, 2.0 and 3.0.
However, there is also .NET framework 3.5 which is somewhat of an oddity. It actually contains framework version 2.0 and 3.0 in one and same package with something new tossed on top of them. So, in the end you only need to download and install .NET Framework 1.1 and 3.5 to have .NET compatibility covered. Then visit Windows or Microsoft Update to get updates for them.
Edit: Almost forgot. .NET Framework is also available for OS X and Linux in the form of Mono.