For younger kids, I love the idea of a backyard circus or carnival - simple games like a ring toss, balloon darts, and a ball throw can all be handmade easily (and inexpensively). Keep the color scheme simple and bright with lots of red and white stripes, and include plenty of carnival foods - popcorn, cotton candy, snow cones, and funnel cakes, to name a few. All of those can easily be purchased or made at home.
For older kids, an outdoor movie is super fun, and can be done fairly easily with a borrowed projector and a white sheet hung between trees. Serve hot dogs, popcorn, and nachos, and send them home with a package of movie candy and a label that says "it was sweet of you to attend the party!".
I am an event planner with a focus on children's parties. I'm new to HubPages, but feel free to check out my upcoming Hubs if you need more ideas.