I have his e-mail password...The account is mostly for job-related purposes so he knows that I check it from time to time.
We have each other's cell phone passwords but I have never checked his messages and he hasn't checked mine (not to my knowledge).
I think some things should definitely be private. I don't mean you have your cell on vibrate because you're cheating type of private... but if trust is lacking in the relationship, this issue will become a huge problem. If he *has* to have your passcodes or vice-versa, I think that is kind of unsettling..?
Also, when a partner wants to step out, nothing will stop him/her. You can obtain a new e-mail account, new cell phone and number, etc. You have to have trust but I guess that is obvious.