Registering as a sex offender is a state statute. Regardless of whether your felony was serious (rape, sexual assault, etc.) or something less threatening (lewdness, downloading Internet porn), registering is required.
If you fail to register, many states still view that as another felony, not just a scheduling mistake. Here's a link to a website called Women Against Registry. The site is dedicated to families of sex offenders who see registry as a hindrance to family reintegration.