An email address is a valuable thing. People don't give them out easily, and for good reason; when you have access to someone's email address, you have access to their lives. If they've parted with this important information and entrusted you with it, they know that they will hear from you again. If they've been willing to do that, you should be honored by the trust you have been shown you and use it responsibly.
If they've given you their email address, it's because of an interest expressed in the product or information that you have to offer. At some level, they want to know more.
This is your chance to tell them more. That email address allows you to put them on your mailing list, and it's the perfect way to get your newsletter out to people, to send out special offers, or just to remind them every now and then that your site is still there, with new, updated, relevant content.
When you build your mailing list, you are not only increasing your customer base and your own business opportunities, but you are providing your viewers with a service. You have something to offer, and one short visit to your site won't exhaust that, so you are really doing a favor to your readers when you send them reminders, with easy clickable links, that you are there and you are willing to offer your products, services and information.
By building your mailing list, you have a chance to build relationships, and when people know and trust you, they'll be willing to do business with you in the future.