If you have a popular name combination, or just get a lot of email at work, you're bound to get an email that wasn't intended for you. You could ignore it, sure, but there are better ways to handle it.
To get some solid tips on how to handle this all-too-common issue, I chatted with someone who's no stranger to getting emails intended for someone else: Liz Miller, who operates the clever Wrong Liz Miller blog. She says she always responds to wrong emails if she can help it:
I even used to have a macro for my standard response: "Wrong Liz Miller — please check your address and try again." It's more of a good karma thing than anything, since it doesn't take too long, but it also (hopefully) ensures that the sender a) figures out their error and b) doesn't repeat it down the line.
So that's all it takes most of the time. The sender will see that they made a mistake and re-send to the right person. Or, if you know who the intended recipient is (like in an office situation), it's fine to forward it to them so they get it in a timely manner. That said, some people don't learn from their mistakes. That's why Miller recommends you hold onto those messages:
My biggest tip with wrong emails is to archive them in a folder/label if you can, because it's a good way to track patterns (i.e. — if you get a lot from the the same people). Also, let's say someone creates an account for a site or service using your email; you may need the original sign-up email (with identifying details) to correct the error.
For frequent offenders who don't take the hint, feel free to block them so your inbox isn't constantly getting filled with to-dos you shouldn't have to waste your time on. At the end of the day, there's no ethical obligation for you to do anything with wrong email, especially if you've already tried to point them in the right direction.