Here's something to add to the list of awesome things you can build for your cat: a catio. It's a portmanteau of cat + patio, and it's an enclosed outdoor space that lets your cat enjoy the great outdoors, without the attendant risks. If you've got the DIY itch, here a few inspiring projects to get you started. Your neighbors may look askance at your new outdoor room, but your cats will be happy, and that's what matters.
Above: This Catio, from The Cat Carpenter, is really just a twist on a screened porch, with slightly larger mesh and shelves for kitties to sit on and look around. Cats can access the catio through a window into the home, humans through the screened door.
Kristin of My Stuff What I Made built this enclosure for her cats against the side of her house.
Barbara from Our Fairfield Home & Garden built this catio, basically just a small screened porch where the cats can play outside (with a door for the humans to clean it).
Mark built this incredibly elaborate cat run, inspired by the one created by the blogger at Cuckoo 4 Design. The cat run consists of several tunnels, enclosed by mesh, which connect a window in his house with a couple of different enclosed spaces where the cats can play around.
David from The Cat Carpenter took an existing outdoor patio and enclosed it in wire mesh, creating a safe space that kitties and humans alike can enjoy.
This large and fairly elaborate Portland catio, spotted on The Columbian, provides outdoor space for eight kitties, and also a pretty sweet place to hang out for people, too.