My kids are still preschool and toddler, but I just wanted to add a small consideration that I remember from when I was a teen. I think your teen should be aware that you might randomly check their room. That way, when you do so they are not shocked and do not feel completely violated. You don't have to tell them when you are going to check, just make sure they are aware that you will.
As far as computers/cell phone, my opinion is that there should be no expectation of privacy. Your teen should be aware that people other than you can hack into systems and that they should never type/share info that they don't want someone else to get a hold of.
If your teen keeps a journal or diary, then I think you should let that be private unless you have evidence of something else amiss (like drug use). I think teens need a way to express themselves and say things that they can't say elsewhere. When I was about 16, I kept a journal and wrote out all my angst. I also wrote fictional fantasy scenarios where I did or said the exact perfect thing or acheived some great honor or whatever. I did not know my mom read my journal. She started reprimanding me for things and telling me that other people were giving her this information. I finally figured out she was reading my journal when she made a special surprise dinner and cake to celebrate my winning a writing contest that did not exist -- it was just a story I made up in my journal. She thought I was keeping things from her. At the time, I was angry because I felt violated and felt she was trying to force her way into my life instead of letting me explain the purpose of my journal before she went reading it. She also made me paranoid that people were watching me and reporting things to her, so I got really distrustful.