I have a garbage bag folded flat in a baggie for an emergency cover. Not pretty but it works.
That's actually a good idea
Living near Seattle - I have to deal with this issue a lot! I have a couple of Coach bags with pebbled leather that look fine after being in the rain. I have some inexpensive bags by Tignanello, Fossil, Liz Claiborne, and a few no name brands that I don't worry about getting rained on. For when I am feeling ultra casual I like Le Sportsac bags - they are nylon (I think) and definitely fine in the rain. Peggy