I've been trying to install ArcGIS 10 on Windows 7 and I kept getting this error. All day long! Frustrating stuff.
Some searching showed that people trying to install iTunes and other applications have also had similar issues.
So what I gathered is, it's a .NET problem. The error message can vary but what you need to look out for is "an error occurred during the installation of assembly..". This article gave me the required clues. The fixes in it are slightly back-dated, so I had to figure something out myself.
For some reason the .NET 3.5 or 3.5 SP1 standalone installer does not run, at all. (I tried running as Administrator etc too). Windows 7 comes with .NET 3.5 which you can remove and re-add (Control Panel > Programs and Features). This seemed to be the only way I could 'reinstall' .NET 3.5, which is required by ArcGIS.
I also installed .NET 4. I'm not sure if this had any effect or not, but after these last two steps, the installations finally completed!