Facebook – How to remove unsolicited posts/spam from the Facebook news feed

Can I "like" a TV show on Facebook but not see news from it in my News Feed?

Yes, you can. Click on the x to the right of any such news item in your feed (it appears when you hover over that item), and choose "Hide [page name]".

This way you retain the "like" status (i.e. continue to be a fan, as it used to be called), but you won't get any more updates from them in your feed.

If you ever want to undo this for some page, you can do that in your news feed options: scroll down to the bottom of your news feed and click "Edit options" (Facebook FAQ item on this).

Facebook keeps on performing some sort of A/B testing, where few users (based on some business logic of facebook) will see one UI, while rest will see other UI.
I don't know how it could be possible at the time this question was posted, but currently you can give a try to these steps:

1. On sidebar of the homepage, you will see 'triple dot' next to News Feed link.
2. Click on this. If you don't have this option, it means right now this feature is not available to you.
3. You will see multiple options here, like:
   i. Prioritize who to see first: Select names of friends whose posts you want to see on the top of your timeline.
   ii. Unfollow people to hide their post: You can unfollow your friends right from here, so that their post will never be displayed on your TL, unless you follow them again.
   iii. Reconnect with people you have unfollowed: If you had previously unfollowed someone, you can refollow them right from here.
   iv. Discover Pages that match your interest: Relevant pages based on your activity will be suggested by facebook. Click like to get their notification.
   v. See more options: If you have any hidden apps then you can manage them from here.
   
   Please have a look at the screenshot: