I'll periodically go down the list and unsubscribe from anyone that has emailed me in the past few months unless I actually enjoyed and found the email useful.
Not perfect, but it does cut it down a bit.
Discussion
Yeah, I usually just ignore the email a few times, swipe it away and it's just added to the ever growing unread. But if it is a noticeably persistent I will get some annoyed that I will unsubscribe, at which point I am now actively pissed off with the company.