Any way that you check your boyfriends text messages without his express permission or him knowing about it, you are gravely violating his trust. Since the stability of a relationship is predicated on trust, be prepared to have it all come un done should you choose to cross that line.
Further, if you do check his messages and hypothetically uncover something incriminating, i.e. He is cheating on you, the only way you can let him know is by telling him you have checked his messages, which makes two wrongs and unfortunately diminishes your angle. There just doesn't seem to be any good that can come of it, if you are experiencing a breakdown in trust it is really important that you communicate with each other.
If your boyfriend makes you feel that you even need to check his messages, there is clearly a trust issue here that needs to be resolved.
I hope this helps.