How can I remove unwanted apps, such as Chess or Address Book, from my Mac? There are a lot of applications that I have no use for that take up space on my Mac that I want to delete. 

When ever I try to delete them it says that it is an essential part of the OS but with Chess.app, I find that reason specious at best.
Select the application you would like to remove and Get Info on it, either Command + i or from the Menu File>Get Info.

At the bottom of the resulting window, in the Sharing &amp; Permissions section, change the "everyone" setting to "Read &amp; Write". You will probably have to click the lock in the lower right corner first and authenticate as an administrator.

Once the setting is change, close the Get Info window.
You should be able to move the application to the Trash without any trouble.