Yes, you do. Usually just some form of identification so that they can match your name. That being said, I have also showed up and just said we had a reservation without having to show ID.
I would print your confirmation numbers and bring to all restaurants. On more then one occasion Disney restaurants could not find our ADR on their list. If you have the confirmation number they can find the ADR in the system.
I learned to do this the hard way. On my husband Birthday a few years ago we had an ADR for Cali Grill. I had to give a credit card to hold the reservation but when we got there they could not find our reservation. They were totally booked and told us we could wait and see if someone in the lounge left but could not get us a dining room table. After fireworks the lounge empty and we got a table there. When I got home I had a no show charge on my credit card I had to fight to get removed.
They have a list of early reservations at the front gate--we just had to give our name and reservation time. I never had to show an ID. As previous posters mentioned, it may not be a bad idea to have your confirmation number. (I didn't print out my confirmations, but I did keep the numbers with me for each day.)
Have fun at the breakfast! The food is great, the characters are fun, and walking though MK with almost no people is truly awesome!