I use cannondale panniers shown in the pictures at the bottom of my post.

The panniers are not water proof. Whenever I go into a store like Publix or Walmart, I grab a couple of umbrella bags from the rack on the way into the store. I put my stuff in these bags, tie it in a knot, and throw it all in the panniers. These umbrella bags are thicker and more durable than the plastic bags they use to put groceries into. My stuff is always 100% dry when I arrive at work even though me and my bike are drenched.