For the time being, the very BEST anti-malware to use is Linux. Why Linux Is Better
Sorry for that but I simply could not resist! Ssshhhh!
In all seriousness now, one must first understand that there is NO such thing as only one Anti-Virus or one Anti-Spyware program that can catch %100 of malware floating around out there. Malware writers are so hard a work that it's impossible for any one company to keep up with it all!! This is why it's so important to use a 'layered' approach.
But before you get rid of the Norton, you should download all the .exe files of the programs that you're going to replace it with and use to augment and compliment each other with.
Here's a list "Armorware" that I can suggest to mitigate against and/or clean up any infestation that you may run into:
--->True: Use only ONE installed on-board AV solution because using two or more can/will cause each to tag the other as viruses due to their definition files containing what looks to each other like viruses, themselves. This is what can slow a computer down to a slug's pace and most likely freeze it solid.
*The only caveat, so far, with AV solutions is Threatfire. Threatfire is in deed in a class of its own (at this time) and can be run along side of and with a 'regular' AV. Since they have two different ways of looking for things and with, more importantly, two different definition databases to draw from one could easily find something the other may miss. Therefore, they back each other up. That's a GOOD thing!
X--->Solution: First, download the .exe of the AV solution of your choice. I, personally, ditched AVG several years ago (when it let my computer get so infested I immediately had to wipe the drive and do an OS re-install!) and, since, have had great luck with Avast Anti-virus. Avast not only protects against viruses, but also against "poisoned web pages" and a smattering of spyware/mal-ware. I have it on my Win box, my room mates box, and three friend's boxes - two of them running XP and one Vista. In addition to me, they all have had very good experiences with Avast.
*After you've downloaded the .exe files of the AV and other progs you choose to replace the Norton [etc.] with, use the Norton Removal Tool given in a previous answer to get rid of your Norton installation.
You can also download CCleaner to clean up any left-over "orphaned files" that the Norton and/or any other program leaves behind. While this is not an anti-malware tool, it is quite a useful utility to find pieces of rogue-ware programs that other programs such as Malwarebytes' may miss and also as a maintenance tool help keep your computer running cleanly and smoothly.
--->True: It is best to run only ONE firewall. Again, firewalls can conflict badly with each other. However, the built-in MS firewall only controls traffic going in ONE direction. One truly needs a firewall that controls traffic going both in to the computer and out of it for maximum protection.
X--->Solution: For this task Comodo Firewall is KING! However, it tries to install a Toolbar and another program that you do NOT need, nor want!!! During installation, if you choose to use it, UNCHECK the Toolbar box and the box for the other program, too. ONLY install the Firewall itself.
--->Anti-malware programs are a bit different than AV programs and Firewalls in that you can install more than one on your computer and it is recommended that you do so. However, only use the 'real-time' protection of ONE of them because the same type of conflicts can occur with that 'real-time' protection that can occur with more than one AV and/or firewall running.
X--->Solutions: Malwarebytes' Anti-Malware ...free version. This is a program the when kept updated on a daily basis can make the difference in cleaning up an infestation and keeping the OS and your files intact ~OR~ having to just wipe the drive and do a clean OS re-install losing all your needed/wanted files along the way. ...(unless you do regular backups to removable media or an external hard drive as you should.)
And Spybot Search & Destroy This is the ONLY free anti-spyware/malware program that offers real-time protection against a myriad of spywarez/malwarez with it's Tea Timer function in addition to protecting your registry from unauthorized/unwanted changes. That said, SS&D has become quite slow, BUT for the protection it gives, it is well WORTH the extra time it takes to Immunize and/or run!!!!
**Once you have chosen the program(s) you want to replace Norton with and have them installed on your computer it's a very good idea to use an on-line malware scanner such as F-Secure Online Scanner to back up your on-board "Armorware Arsenal". This particular one not only finds infestations, but allows you to clean them up as well. You even have the choice to allow it to Automatically Clean or Manually Clean what it finds, if anything. (Strongly suggest the Manual Option.) The reason to use an on-line scanner is that there are certain types of mal-ware running around out there that have the ability to, not only get past your on-board arsenal, but shut it down! By using an on-line scanner you can periodically check to make sure your on-board arsenal is working. AND if any of your on-board real-time arsenal 'cries' you can clean your computer with all of the on-board arsenal and then double-check with the on-line scanner.
***In addition to all of that, because while IE is getting better it still hasn't quite caught up yet, Security-wise. You should replace it along with your Norton. Instead of IE (!!!do NOT try to uninstall IE!!!) you can use Firefox, instead. Simply make Firefox your "Default Browser" if/when you install it. There are some very good Add-ons for Firefox that can help you in the fight against malware. The most important ones are:
WOT (you can get WOT for IE, too, in case you insist upon using IE.)
There are also some Add-ons that just plain come in quite handy! Like for instance:
Unsorted Bookmarks Folder Menu
Yahoo! Toolbar (if you use Yahoo!)
You will find that there are scads of Add-ons and Themes to choose from for Firefox so you can "build your own browser"! The 'Classic Compact' Theme takes up less space on your screen than ANY of the rest. You can even choose "skins" for Firefox with Personas Plus.
X---> Just remember that:
1. All the anti-malware programs in the world are NOT going to do any good at all if they are not KEPT UPDATED and manually used on a regular basis...at LEAST weekly if not more often.
2. There is a LOT to be said for staying out of the "back alleys" of the internet, also being quite careful of social networking sites and "Best Practices" when is comes to the use e-mail (E.G.: NOT even opening spam and/or e-mail from those you do not know and NOT downloading attachments unless you know the computer habits of those sending them to you just to mention a couple of those "Best Practices".)
I hope this helps give you some intriguing options and helps you out, Carol. Good Luck!