Bob Carne wants to use Trend Micro Internet Security as added spyware protection, along with Norton 360. They don't play well together.
It's generally not a good idea to have two full-bore security suites such as Trend Micro and Norton running together. It's like two people trying to use the kitchen sink at the same time. Besdies, one of these programs on it's own is enough of a drag on your system.
If you want to supplement Norton with extra spyware protection (and that's a very good idea), I recommend SUPERAntiSpyware. If you just want to do an occasional scan, the free version is fine. If you want real-time protection, spring for the $30 Professional edition.
And don't get upset if whatever spyware detector you use keeps finding infections--at least not until you've looked at what those infections are. Almost all of them are probably tracking cookies, which are a natural result of surfing the Web. While technically spyware, tracking cookies really are not all that scary. See Block Spying Cookies, but Keep the Helpful Ones.