Area rugs can both define your outdoor space and give it personality and depth. Not to mention adding comfort and cleanliness.
Use the same sizing rules as you would with indoor area rugs: go bigger than your gut (and wallet) tells you, all front furniture legs should overlap the rug by at least 4 inches.
What material should your rug be made of?
If your outdoor space is under a permanent roof, you have a lot of options. Pretty much anything with a loose enough weave and no backing should work. Even if the rug won’t get directly rained on, it will be exposed to more moisture than an indoor rug and needs to have decent air circulation to prevent mold.
Yes, your conclusion is correct, no shag rugs outdoors. Sorry.
If your ourdoor space is en plein air, there are a few more restrictions. Seriously consider something made out of a synthetic material. I know it doesn’t appeal to the naturalist in you, but neither will throwing out your moldy jute rug.
Outdoor Plants
This seems like a no-brainer, but you would be surprised by how many outdoor spaces are completely lacking any greenery. There are loads of options here. Understand that potted trees are just as fantastic outdoors as they are indoors.