I try to remember to bring my own bag, but I do forget sometimes. I think over time I'll get better at it. I only started bringing my own about a year ago, and habits tend to take a while for me to develop.
I do take the plastic bags when I forget, but I always save them and reuse them. I use them when cleaning out my cat litter, or as trash bags for the bathroom.
My apartment complex supplies biodegradeable doggie bags for residents. I'd like to get to the point where any plastic bags I'm using are the degradable kind.