I don't look at his e-mails, even though we know each others passwords... once or twice we've had the other person look for something in our e-mails if we're away from the computer, so I think
for us it's worth knowing the passwords, but I do assume he'll never look at my e-mails otherwise!
I have sent instant messages back for him when he's asked ("hey honey, I think I just got an IM, if it's Dennis let him know we'll be over at 4pm!") or back in the day when we played World of Warcraft, if I was doing something on his account and someone messaged "him," I'd reply to them. But I always explained why he couldn't do it at the time, hoping people wouldn't think it was TOO weird.
I still HATE answering his phone, though, even if he wants me to... that's just too awkward to me... but his sister and her husband seem to answer each other's phones all the time.