Blinded, I would consider myself in a normal relationship.
I absolutely trust my DH that he wouldn't cheat. I know that he looks at porn from time to time (i dont like it, and he knows that, but i think he probably still looks) and that he probably had a lap dance on his stag. But that's it.
I have never had any cause to check passwords for his e-mail, because both our e-mails come into the same account. Similarly, all of our accounts and credit cards are either joint or completely transparent (which given my London spend-fest this weekend, is not always a good thing
).
Both fb accounts are completely open, not a big deal if they are left logged in, and in fact the only secretive aspect of our relationship is me on MN, he knows that this is somewhere that I consider my personal space, and he respects that. He doesn't know my nn, or anything else. He also knows that I don't like him looking at my text messages, not that there is anything weird in them, but that I would feel violated if he were to casually browse through them. Neither of us have ever felt the need to delete messages, although again, I reckon DH uses private browsing for porn.
I don't post this to sound smug, and dear knows, we have our difficulties at times, but cheating and secrecy are not one of our issues (touch wood). The reason I post is to show what normal is like.