Any suggestions on cat-proofing my house plants?

I love cats. I love plants.

Unfortunately, these two things do not always go well together.

Does anyone have any suggestions on how to kitty-proof house plants? She's not usually interested in the plants themselves, but LOVES digging in the dirt and knocking pots over.

Would it harm most indoor plants to have plastic stretched over the dirt? (I grew up in a desert and now live in Oregon, which means I tend to over-water and give my plants root rot. Would covering the dirt make that worse?)

Would be grateful for any suggestions!