I'm not sure if anyone is experiencing this, but it has been happening to me for a while.  I get weird e-mails saying:

It's probably not directly linked to this site. You include your name in your profile, so someone who looks up your name on Google will find your profile on chess.com. The email address was likely obtained in other ways.

it is likely that you posted your email address visit on the website somewhere. maybe on your profile, or in a group, or something. evil spiders crawl the web and look for email addresses posted on the web... message me your email address and i'll take a look. 

You can usually avoid the "bots" which troll for email addies by only giving yours in PMs or notes to those you trust, or converting the "@" to "AT" and the "." to "DOT" so they don't recognize it as an email if you must post it on an open board (although with the internal messaging here, you shouldn't need to ever do that).