Brody's Mum, that's a really hard question! I'm trying to think room by room.

What's priceless at my house? Priceless = not easily replaced, in my mind. So I'd have to say the following...
-The contents of my top left dresser drawer - my degree certificates from high school, college, graduate school; the Bible I received for my eighth grade graduation; several handkerchiefs that were my grandmother's; and a stash of photos.
-Curio cabinet - the hula girl music box my grandmother brought home from Hawaii. When we visited her when I was little, she'd let me take it off the shelf and then she would set it in motion for me. Looking at it reminds me of those visits. More family photographs but these are school pictures of my nieces and they're in frames.
-Bedroom closet - big box of photographs. Little box of photographs - some from my grandmother's house, family snaps from before I was born. I really should get those into proper storage with acid-free paper.
-Kitchen - two pictures on the wall. One is my youngest niece's hand prints in red paint, and two purple hearts, which she made in pre-school. The other is a water color my second youngest niece made in pre-school. Those should probably go in proper storage, now that I think about it. My nieces are 16 now and the pictures were done when they were five.

I agree with Lilith about the pictures. My sister's former next door neighbors had a house fire and lost just about all their family photos. After that my sister had copies of her wedding photos made and put in a lock box at the bank, just in case.