This has happened to me quite a lot over the years. I've had my gmail address since 2004 and it is just firstname.lastname@example.org (it is an uncommon last name - every person I've encountered with the same has ended up being a distant relative).
If it seems to be a genuine important email, I will try to figure out the intended recipient or try contacting the sender. I've gotten medical appointments, dental appointments, stuff from lawyers, seemingly important orders for an artist (she seemed to be a very nice lady but her name was nothing like mine so no idea how she ended up using my email), etc. There have been plenty of other random ones (letting "Sue" know when the next choir practice was, etc).
The most troubling was a couple emails from Qantas about my flights that included links to modify/cancel the bookings. I did follow the links to see if I could figure out how to contact the actual customer and it did look like I could freely modify/cancel the booking without any further validation. I could not find contact info for the customer but did contact Qantas - it took them about a year (3 times reporting the issue) to remove my email from the account. As far as I know, they have not added any extra security (makes me WAY less likely to fly Qantas).
The most annoying was someone named "Samuel" who used my email to sign up for "every" payday loan service (for months, I got a slowly decreasing slew of spam from them (starting at over 100 emails per day)). Absolutely none of the services used any sort of email verification. A couple years later, he used my email again a few times (again for payday loans and something else but, fortunately, only a couple payday loan places this time).