In my experience, it's mostly the situations where people give their emails in person that are a problem: Receipts from in-store purchases (and in-store credit card signups), hotel reservations and rewards programs, EMR signups, lawyers offices, banks, realtors, etc.
Websites are pretty good at verifying email addresses these days. The real world, not so much. The super funny part is when you try to ask the bank/doctor/etc. to stop sending someone else's personal info to your email address, and they tell you they can't make that change since you aren't the account owner.
Another possibility is that companies try to guess your email address. I recently got an email thanking me for buying a lawnmower that I never bought. The buyer's mailing address was in the email, so I sent him a letter. He replied saying he's "old school", and doesn't have an email account. He has no idea how the manufacturer got my email address, as he had left the email address field blank when filling out the warranty form. The only explanation I can come up with is that they just guessed it based on first and last name.
I personally find this Gmail feature (as well as the ability to append +anything to your email address) extremely useful.