I have had this happen a few times, and I always reply with a note that they are sending this to an unintended user. Once, it was someone's tax information. Usually if it is important communication, one reply will cause them to correct it in their address book. Mail coming via listserv is more difficult to get changed, so you can set an email rule that will auto delete the message based on the sender (ie, @listserv.church.org)
For creating web accounts, you can make an email that you don't really use for other communication (ie, myfacebookemail2468@gmail.com) so it is less likely you will run into others using that email, and it will cut down on spam you get when that website sells your email.
I think it is always important to have at least one email from a free account, like gmail, because you may change jobs and lose that account, or you may graduate from that school and lose that account, or change ISP's and lose that account. But try to make a username that is descriptive and easily remembered coachbob@gmail.com is better than B.L.Smith@gmail.com