.NET Frameworks 1.0, 1.1, and 2.0 were all cumulative and self contained. Then I stopped paying attention, and apparently .NET Framework 3.0 marked the beginning of the supplemental versions that build on 2.0 and require 2.0 to remain installed. I only assume .NET Framework 3.5 will be the same way.
So you shouldn't need any of the 1.x series installed, but you will need 2.0. Though some people seem to claim that older .NET apps written for the 1.x series don't always work well on 2.0. Last I checked Microsoft was still offering the .NET Framework 1.1 download via Windows Update, so it'd just a small additional hassle to reinstall it if you remove it and run into one of these apps I suppose.
...need I keep older versions on my PC or can I uninstall them? I wouldn't see why they'd be needed, but a friend says that I should leave them there.