These instructions are for the regular version of Facebook, not the mobile version.
Go to http://www.facebook.com/?sk=app_2309869772&cs=2 (that's the Facebook link app). You could have hundreds of links here or just a few.
First, if you want to quit liking a link and you have previously liked a link, there should be an Unlike link. That answers your question, but if that is not what your really want, there is another option.
If you don't want any links from a particular page, group, or person, you may hover over the link until there is a blue x in the upper right hand corner. Click the x and you will be given the option to [Mark as Spam] [Hide (page, group, or person] or [Cancel]. If you mark as spam, it will send a report to be reviewed by Facebook and delete the link. If you choose to hide, you will get no posts or news from that page, group, or person. If you don't like those options hit cancel.
The third option is to hide apps that share links. If a person is using an app to share a link or other silly information like I just got a pig in Farmville, You may be given another button that says [Hide (some app)] without hiding your friend.
Finally, if none of those work, you cannot hide just one post without hiding the poster. Search for a page or group on Facebook that says, "I want a choice to hide a post without blocking a friend or reporting as spam," and Like it or Join it.
Experience is my source.