ZenCart newsletter subscriptions generally require a person to sign up for an account (at which point they opt in or out of the newsletter).
There's a newsletter-only contribution in the downloads section under 'other modules' that will allow newsletter-only subscriptions, if this is what you are looking for. It's for ZenCart v1.3+. I'll be releasing an update, hopefully tonight, but more likely in the next day or so that fixes a few known issues (see my site or the contrib thread) and adds a few new features.
-Ng_



