An admin of the event has the option to delete the event among other editing options.
To remove it from your events as a user you can change your RSVP to not attending.
Yes you can completely delete your Facebook page via Facebook page manager. You just have to leave the reason of deactivating you page.
To remove a fan page on your facebook account you can Unlike them by simply visiting the fan page you want to remove you can see the "unlike" link at the bottom part of the page. But if you own the page you can delete it permanently just use facebook as page and go to "edit page" and click "Permanently delete this page".
The Facebook can delete her/him from facebook if he/she has been reported few times. You can remove a friend from your friends list by going to a friend's page and at bottom left corner there's a Remove button.
Go to Facebook and go to your Account Settings, then go to the Apps tab, from there find Answers.com and remove it. That should do it.
Go to settings >profile> on the lower portion of the page look for Facebook there check "Disconnect".
Go to your wall (click "Profile" then "Wall"), and you can click "Remove" next to the post.
The person who visit your Facebook page are generally located on your friends list. If you suspect that a person is viewing your Facebook profile and you don't want them to, remove them from your list or set your page to private.
Around mid-way down the page on the left hand side of the person's profile page, there's an option: remove from friends
If the Facebook invitation is to an event or something similar a user can just select decline. If you have been added to page or group, a user can just unlike, leave, or whatever option is given.
message them and ask them to remove it
Assuming you want to remove yourself from being a fan of the page--Go to the page in question, scroll down and look on the left-hand side of the page. Click the link that says "Remove me from fans".
On your facebook page click on Account then click on Application Settings you can then click on the X by the application you wish to remove.