I’ve seen a few folks who’ve had trouble installing ArcGIS 10 because they’ve been unable to uninstall ArcReader (usually version 9.x).
The best way I’ve found to do this is to download the ArcReader installer from here. Run the installer and try to uninstall.
If you’re unable to do that (sometimes you’ll need to force quit and restart) you may need to run an install, but uncheck the ArcReader feature. This gets rid of some hanging installer memory.
Then try to run a repair (restart if necessary) and start the downloaded ArcReader installer … select repair when prompted.
After you’ve repaired you should be able to uninstall correctly.
If that doesn’t work, you’re stuck deleting all ArcReader files and ArcReader (and ArcGIS/Esri) references in the registry using regedit.