I'd feel extremeeeeeeeeeeely uncomfortable giving someone else my password, or even them using my computer!
I think we once discussed here about couples using one email!? and some of us felt like it was like sharing a toothbrush... grosss. Although it does seem like most couples end up sharing their passwords.
I have no problem with someone coming and sitting next to me and us looking through our email together though (which i do with my bro or sis sometimes, or friends). I have a freak files folder though, so it is entertaining
Maybe if you want to spy, just go and sit next to him or look over his shoulder and ask him 'oh what's that email about?' ewww it's a dating service! delete that and watch to make sure he does it