It is as has been said
The web site company you visit can only send you email if you provide them with an email address.
That said, we always tell posters here never to include their email addresses in posts in Public Forums or elsewhere on the internet, blog comments and such, as robots trawl those to farm email addresses so they can be sparmed.
If you have proper email software or even recognised web based email such as GMail, Yahoo Mail and so on, they all have protection for email users. For example my Thunderbird email software won't load images in an email unless I allow it, and will tell me if an email has a potential risk, ie it will tell me if it thinks an email is a scam. But no email software or web based email can protect against all risks and that's left up to us.
However, emails from recognised companies like Amazon, HP and so on are considered safe, but I agree with you, unless you are sure the email is from a recognised source, do not click any links in it. Such scams include emails that demand you click a link to confirm your username and password. Established companies never do that.
In your case, visit the web site in your browser by typing the address in the address bar, log in, then look in your account options for email preferences and untick all you don't want like promotions and such.