I know two people who had girlfriends like this. Rather than dealing with the problem, they assumed that she would change. They ended up getting married and now they're miserable with a kid. A boyfriend, girlfriend, husband or wife is meant to be your equal partner and trust is key. You wouldn't go rock climbing with someone you didn't trust, why would you possibly spend you life with someone like this.
You *need* to talk to her about this. Listen to her concerns, because clearly she has a ton of insecurity, and ask how you can make her feel more secure (without giving up your freedom to be an adult). Give her time, but if she can't change, you need to consider saying goodbye.
If you're not happy, whats the point?