When attempting to install the RTM version of .NET 3.0 Framework, it would fail almost immediately. Looking in the Event Viewer logs, it was complaining that it couldn't write to the machine.config file (and later on, the web.config file). Apparently, it needs to make some changes to these files, and they are usually read-only (it isn't clear to me why the installer didn't have rights to change the permissions on the files).
By changing the permissions, the installation succeeded.