Respect is really important to me here, and it's a two-way street.
I believe in implied trust a lot. If I'm hanging out with a girl and she's on Facebook and some guy messages her, I'm not creeping over her shoulder trying to read the convo, or asking her about him. I don't care who she talks to because I'm secure where I'm at.
The same goes with girls. If I get a text, first of all I won't read it in front of her, I don't respond to that stuff when I'm with girls, if I expect her to keep her phone put away than I reciprocate the favor.
If the girl is all up in your business than she really isn't relationship material anyway. The best girls I've been with are the ones where you don't even need to hide your phone around them, you can confidently leave it out in the open unlocked and not worry about her going through the past 6 months of text messages.
For the record everyone should have a lock-code on their phone of some nature. I have access to all my bank accounts, my trading account, all my personal communication, my e-mail, and a ton of other stuff right on the phone. You bet my phone locks after a few minutes of idling, I don't want a thief taking over my life.