Since newsletters are legally required to have an unsubscribe option somewhere, that gives them a unifying word that you can filter out!
1. Go to your filters (click the gear, click settings, then click filters). Scroll to the bottom and click "Create a new filter."
2. Under "Has the words," write "Unsubscribe," then hit "Create filter with this search."
3. Mark "Skip the inbox (Archive it)."
4. Mark "Apply the label" and create a label called "read/review" or something similar.
This way, you can glance at anything that's automated all at once when you go to your read/review label, rather than having it bother you in your inbox.
If you want to continue receiving some of these emails in your inbox (say, notifications from Facebook and Twitter), you can just edit the filter to create exceptions for those words (i.e., put "Facebook" "Twitter" under the "Doesn't have" field).