Should couples share their passwords? What about after marriage?

I was speaking with a co-worker and she said that she and her husband share all of their passwords (phone, email, banking, facebook, etc.). Is this normal for couples who are married?

One argument is that there should be trust between each other, but another is that if you have nothing to hide then why does it matter? In a long term relationship or marriage, will someone be offended if you ask to have their passwords? What if you voluntarily give yours first?