In future if you have a prob, it helps to post your model of Mac and it's operating system & any other tech details that you may feel is relevant.
All of the below only counts if you have OSX, some of it OS 9.
If I were you I would remove it.
Norton Utilities has screwed up 2 of my hard-drives in the past, Norton Antivirus is a waste of time on a Mac and can lead to conflicts with other programs.
Do a forum search on Norton Utilities to find out others' experiences with it.
You won't find many complementary comments.
You may not have to remove it. If you're running OS X, go to System Preferences, Accounts, Startup Items tab. See what apps you have there (these auto-start when you boot the Mac) if Norton or anything unwanted is there, except for Suitcase (if you have it) then deactivate it.
If that fails trash it, especially if you have the original installation CD.