Have you just sent a friend request to someone who you don’t want to be friends with? You can remove the request by going to Account>Edit Friends>All Connections, or simply to this link:
http://www.facebook.com/friends/?filter=ac
Now, use the next button, if you have to, to find the person that you mistakenly sent request to. Then click the cross next to their name as shown below:
The person will not see the friend request anymore. But if they have subscribed via emails to Facebook notifications, they will see the email because the email is sent almost immediately when we send a request and there is nothing we can do about it.