At the most Avast tells me when it updates the virus definitions or when it there are new program updates available for download all of which I'm sure you could probably turn off.
You really ought to get rid of Norton as it's such a resource hog. I switched to AVG per the advice of a friend as he said Avast wasn't capable of catching some things.
MMM... I don't mind Norton's to be honest. 2008 isn't a resource hog or resource draing as previous versions. I found the footprint to be quite minimal. Plus, the folks at Symantec have always been really nice to us at WorldSims when we were small.