A number of my friends, who I otherwise enjoy seeing content from often share content from a particular page that I don't care to see ever again. Is there a way to block content from a page?
There is absolutely no straight-forward or proper way of doing this.
You Can block People, Games and Apps but not Pages.
All you can do is unsubscribe the friend who posts such contents, or subscribe to only "Important Updates" from the particular friend:
You can try clicking on either "Hide Story" or "Report Story or Spam" to give hints to Facebook that you do not like the content of a particular page.
All these would reduce the probability of such posts appearing in your "News Feed".
If its not a direct status update or share from a friend, but the result of a friend posting a comment directly to the page itself, then you can block it from your news feed. Hover over the name of the Page when it appears in your Newsfeed (it will be in bold type). A down arrow will appear. Click on it and select "Hide". You will then be given the option to hide all comments made on that Page.
If it is a direct status or share posted on your friend's page, then you cannot hide it without hiding all updates from your friend.
An easy way to hide page updates, where your friend has commented on a page, or liked a post on a page, that you dont want to see, is to use a newsfeed filtering browser extension, such as FB Purity. It lets you type in keywords or phrases, that you dont want to see in your newsfeed and then it filters them out. In this case, you would just need to put the name of the Page whose posts you dont want to see into the extension's Custom Text Filter. You can get FB Purity here: http://www.fbpurity.com
Trying clicking on "Pages feed" from your news feed page. (It's part of the list of things on the left hand side)
It will bring up the pages you've got auto-posting, if you got to the down arrow at the top right corner of the first post, click on it and choose "Remove this post" (or whatever it says), it then gives you the option of removing the entire feed.
I clicked on "like" for one of these things and got swamped!