Yes I mind because that's child's play. if you're in a relationship, trust should be one of the key factors. if your relationship requires either OR both parties checking each others phones, not only is that being insecure but it defeats the purpose of having a relationship! If I were you, I would re-evaluate my relationship.
If you love your girlfriend and she is your life.Then everything in your life she can check and see and want clarification from you and you have to clarify her like mobile...
Regardless of whether you have something to hide on your phone or not, it's something private, especially if it is a smartphone. It can contain your personal diary in form of notes you take, your personal thoughts scribbled down that you wouldn't want to share with anyone in the world, your contacts and messaging records which - despite not having anything you'd want to keep from your partner - you wouldn't want anyone to go through, and the list goes on. And then there could be business related information which is simply none of your partner's business. I use a note taking system which synchronizes notes between my work computer, my smartphone and my laptop. Many of those notes include information on my projects, their budgeting, what I've made in each project, how much of it am I paying and how much is saved, my expense record, and so on... If my partner goes through that data and questions me about any of my expenses etc. she has nothing to do with, I will definitely not be pleased. It can cause confusions needlessly. If there exists a bond of trust between a couple, going through the partner's personal data can only weaken it.
I never really minded my phone being checked, I have nothing to hide. But it is insulting if they check, almost as if they don't trust you. There should be no need to invade someone's privacy really, especially if there is trust.