Yes,you can hide your facebook profile from facebook search.Basically facebook provides you with three options as follows:-
1. Everyone can search your profile on facebook
2. Only Your friends and friends of friends can search your profile
3. Only your friends can search your profile
For those who are really frustrated by daily unwanted friends request should select either 2 or 3 option.
Here is the complete step by step tutorial with screenshots on How To Hide Your Profile On Facebook
1. Login into your facebook account.
2. Click on Account on top right side.