Norton is a useless piece of trashware, it couldn't find its ass with two hands and a GPS device. About the only things it does are a. fuck up your system files, b. install a couple useless, resource hogging services, c. insert an obnoxious, worthless little widget into your taskbar, and d. make itself extremely difficult to remove. Sound like any other particular category of software you can think of? Yeah. That's right.
About 80% of the virus removal jobs I've done are on systems running either Norton or McAfee, and honestly they were harder to completely remove than the viruses in many cases (the shit that Norton 2003 used to do to the registry, in particular, was a nightmare to clear out if its regular uninstaller was broken, somewhere around 500 entries to be removed by hand).
All ranting aside though antiviruses will not pick up a lot of "gray area" spyware & malware, particularly the kind that comes installed as a component of crappy shareware, that's why you run a seperate spyware scanner. Also of note spyware scanners pick up a lot of relatively benign things like tracking cookies, and some of them even MRU lists (for "privacy" reasons), which are not, I repeat, not malware and should not be confused for it or be frightened about.
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Back to the topic at hand, unless your (hopefully non-piece of shit) antivirus is picking up a lot of other viruses consistently for no apparent reason on its regular scans you can be pretty sure wininit.exe is legitimate, since one major symptom of a backdoor/downloader type virus is that it will enjoy downloading a variety of other viruses.
Another way to tell is to look at its location, if it is running from c:/windows/ it is legitimate, if it is from any other folder it isn't.
One thing to note if it is legit, but you see it running all the time: there is something wrong with one of the programs you have running at startup. Wininit.exe should shutdown within a couple minutes of windows starting up, after it's completed running all your startup tasks. If it's taking longer than 5 minutes something is hanging or otherwise screwed up.