You sure can, but Josh Wiener, builder and president of the contractor firm SilverLining, says to make sure your counters and appliances extend four inches up the wall at the back. When a pan bangs the wall behind it, the lip will shield the wall from getting dented. And when you spill something, it will keep the liquid from making direct contact with the wall itself.
If you do use paint, Wiener says it’s necessary to use an excellent primer that is moisture-resistant and paint that is proven to be cleanable. He also says not to use a matte finish, but a semi-gloss or above for durability and ease of cleaning.