Hell no! Maybe if I was married, but even then I wouldn't see the necessity behind it.
If you're getting the feeling in your gut where you need to check your girlfriend's email and cell phone, and you're not completely paranoid/insane.. Then something's probably up.
In the end I guess, it's all about what you want. If you're cool with this and don't see it as a big deal, then it's not. If you're not cool with it and you enjoy your right to privacy, then it is a big deal. I'm sure every guy no matter how long he's been married will have a phone conversation, text conversation, or send some emails that could put him in hot water.. Same goes with the woman, even though they may not even be a big deal (they could be misinterpreted too).. I'd say it's best to let both people have their privacy in those worlds. If something's up, you'll feel it in your gut.