I am going to assume she uses Hotmail, Gmail, Yahoo or another one of these hosted email accounts. Does she have an email account on the home computer such as Outlook or Outlook express? If so, chances are she uses the same password. Use a program called behind the asterisk on Outlook or Outlook Express to find out the password and then try the password on her 3rd party hosted email account (Google, Yahoo etc). If that doesn't work then the only real option you have is a keylogger. A keylogger might be your best answer anyways, this way you can see her MSN, Yahoo chat sessions. If she is doing anything behind your back, chances are she uses a chat program. All you need to do is tell her you are going out for a few hours and I guarantee you if she is cheating on you, she will jump on the computer to chat with her boyfriend. Then you will have her chat on record.
To all other negative commenters, it is not our place to judge why he might choose this method, it is our job to answer his question. What he does with the information is up to him, he has to live with the consequences.
If somebody asks how to make a bomb here do you think we should blindly provide the information without considering what he might do with it?
He aint asking to make a bomb, he is simply trying to find out if his wife is cheating on him, which he has every right to know. There should be no secrets in a healthy marriage and if he asks her to open the email accounts in front of him and she doesnt, then yes he has every right to know why she doesnt want him seeing whats in her email.