After reading about this fun art party on Birthday Girl, I started thinking about placemat invitations.
For the art party, the mom created a coloring sheet invitation. If you'd like to try making your own coloring sheets, you can make some using your own photos, which would be fun for a party invitation, or you can draw your own.
My friend Julie creates her own placemats for her kiddos all the time. She simply takes their art work, or other pictures and uses laminating paper to cover them and make them water resistant, read: easy to clean. An even cheaper way to do this is to use clear contact paper. It's not as stiff as laminating paper, and won't last forever, but for invitations it would probably serve your purpose.
This would be great for a kids in the kitchen party (which I happen to be planning right now), or any themed party. On the front of the placemat, you might have your invitation details. I would just use Publisher or whatever program you usually use to create the invite, and use that for the front. The back could have some fun games pertaining to the theme. For kids in the kitchen, you might have an easy recipe, a simple fraction activity, etc. For any theme, I think a word search would be a fun addition. This site allows you to create your own word search. So, for a cooking party, you could use cooking words like apron, flour, eggs, etc. Add a connect the dots picture to the back also. The idea is to have a few activities the kids can do that pertain to your theme, whatever it is.
If you'd like, you can include a dry erase marker with your invitation. To take it one step further, you could add a piece of velcro to the placemat and marker to keep them together.