Obviously if somebody knows your email address nothing stops them from registering them to a site. But there appears to be some kind of effort to register mine to a lot. So far I see 1750 "welcome to our site" type of emails within the past hour.<p>Has anyone dealt with this before? What should I look out for?
I run an email newsletter company and deal with bad actors on a daily basis doing this. As justinludwig says, a common reason for this is to flood your inbox so you miss other important emails (often banking related ones). We've also recently seen a huge increase in attempts from Russian IPs doing it for seemingly random reasons. You may also have fallen out with someone/a customer who has thrown your email into such lists just to cause you a headache. Most good systems will have mitigations in place to prevent/reduce this (we use a range of IP reputation and other mechanisms to nip it in the bud quickly) but enough don't for it to still work.
This tactic is usually used as a diversion, either to bury an important email message (like a notification that your credentials to an important account have changed) in a flood of garbage messages, or to keep you focused on your email instead of keeping tabs on your usual responsibilities (like say to monitor the entrance to your office suite).