My daughter has face book, she got it when she was 14, she will be 15 in nov.
I set it up for her and she knows I have all her pass words, she knows I can go on it and she is NOT allowed to change them.
She also just got a cell phone last year even though I didnt really want her to have one yet and I also have the passwords to that to, which she is NOT allowed to change.
That being said I have rarely gone on her page to monitor her activity, she knows I can and we are close so I havent had much need. Now mind you I HAVE been on it and HAVE gone through her phone but again not often and sometimes its been with or without her knowledge. I even post pics for her etc.
Now in my case my daughter is a minor and she knows phones and facebook are to be open to me at all times. Thats just how it works she is a monir and she is mine but she is also a VERY OBNOXIOUSLY GOOD KID lol so I dont have many worries.
I would NOT do this to an adult child, even under my roof, the relationship should be good enough to share stuff that is important and for them to understand that by time they are 18.