Liking something has never been easier. Most Internet sites have Facebook like buttons embedded on their pages which you can click on to like a page. Plus, you can also share a page on Facebook directly with your friends and contacts, which counts as a like as well.
It is however not as easy to unlike what you have liked, especially not so since Facebook made it rather difficulty to display all the likes on a page. And do not get me started on trying to unlike one of the pages that you have liked before.
To unlike, you need to head over to the page on Facebook, click on the Like button there, and select the unlike option from the context menu. Imaging having to do that for hundreds of likes that you have given out throughout the years.
You can display a list of all of your likes on your favorites page which you can access here: https://www.facebook.com/username/favorites
Make sure you change username to your username on Facebook.
An alternative is the Facebook app Allll my Likes which is an app that does not require permissions to display your list of liked pages on the social networking site. Once installed, you will see an ordered list of all Facebook Pages that you have liked in the past.

Each page is listed with its number of likes and a link to the Facebook page where you can easily unlike it. Plus, you can also unlike the pages right in the listing which is way more comfortable, especially if you have to go through hundreds of likes.
Once you are finished up with the page like cleanup on Facebook, you can remove the application again. This can be done on the left sidebar where the app should be displayed. Just hover over it with your mouse, click on the edit button that appears and select remove app from the context menu.