For me, I still prefer to have the hard copies mailed to me. It just is an extra reminder for me that there's a bill to pay. It's too easy (for me) to lose things in the ocean of email that I get and even though I go through it semi-regularly, my email provider still has the tendency to filter real email into the junk mail folder.
We have a cross-cut paper shredder at home, so we just shred the bills when they are paid and we don't need the paper statements any more.