You probably have a lot of two-dimensional physical objects around your home or saved in file drawers or boxes which have sentimental value, but which you don't actually want to have on your walls. Children's drawings, posters or flyers from shows you went to, holiday picture cards from friends, etc. can pile up.
You do not need to keep a physical archive of every significant image that comes into your life.
But you may want to remember things and have the chance to look back at them later, so take a picture, back up the digital copy, and get rid of the stacks of papers.
I find that a lot of these things I keep, have a story that goes with them, so I like to put the picture up in my weblog (I use TypePad) or into Flickr, the photo community site where I can write a bit about it. It's also easy for me to share my stories with friends and family that way.
One other nice feature of Flickr is that it is easy to collect things into sets. You could even get a little book printed of those images. A stack of every drawing your kid made this year might be a bit much to hold onto, but a yearbook of your favorites along with other photos of your kid from that time period might be one of the most wonderful souvenirs you could have.
I'd recommend also digitizing the things you do have on display in your home. If it should ever suffer damage, it's nice to know that you have a backup digital copy as well as one you can easily access on the web.
And by the way, you can do this with little tchotchkes too. Don't really want to keep that big collection of refrigerator magnets, but it'd be nice to remember the glory days when it covered the entire front of your fridge? Take some photos, maybe keep a handful of favorites, and sell the rest at your next yard sale. (Just don't set the bag of 'em next to the hard drive where you've got all those backups, okay?)