I told my DD when she was 13 that I would check her Facebook and phone if I wanted to, wouldn't have done it without telling her, I did the same for her older brother, to be honest I hardly looked at his he was never into the social media stuff. DD made some very bad choices at 13/14 we had two years of constant drama and worry so I needed to know what she was up to. To be honest I still have her passwords but she is 16 now and seems to have settled down loads I never look at it.
My dmum 'couldn't help looking' through my personal stuff when I was a teenager. Inevitably she eventually found something that she felt she couldn't ignore and I found out that she had been snooping. It did irrevocable, enduring damage to our relationship. The irony was that she had got the wrong end of the stick and it was all totally innocent Obviously she's your daughter and you want to protect her, but please don't let it be at the expense of your relationship.
Also both my DDs would go cat if they thought Mummy was spying in them and I'd find out absolutely nothing.
Far better teens feel happy to chatter to you than think you do trust them and are watching their every move.
Think back to when you were 13, you didn't have the Internet, but did your parents know where you went on your bike, who you called on the house phone or from the telephone kiosk. Did you come straight home from school or go to the village disco. Did your tell your parents exactly which friends you were seeing. Of course you didn't.
Do you know what your teen is up to all the time? Since getting an iPad I now have unrestricted access to DD's FB, Twitter, Instagram and other online shite as it has not dawned on her that as she first logged in on these it automatically goes into her accounts not mine. This means that I can read all her private messages etc. She is exchanging lovey dovey messages with a boy from school and I have discovered that she and a friend went to meet him on Saturday tea time. I don't mind her not telling me if she has a 'boyfriend' BUT we had a big falling out last night as she had not brought her phone downstairs before going to sleep. She messaged this boy this morning before leaving for school, but HOW???? I had her phone and her laptop and my ipad so how the hell is she getting on line? I don't want to tell her that I have access to her accounts as I prefer to keep a check on what is going on. Or am I being too nosey and should let her get on with it. The only thing I can't access is her phone as she has it password protected.
Disclaimer, she is by and large a good girl (I hope that remark will not come back to bite me on the bum) just very moody since becoming 13.