Styrofoam is not biodegradable, which means that it will stay on the earth FOREVER. Some coffee shops are trying to be better about this. On the Starbucks disposable cups they state that 10% of the cup comes from recycled materials and the sleeve 60%. Many coffee shops will give you a regular mug if you are going to stay in the shop and drink it. Leaf and Bean will do it, you just have to ask them. Some coffee shops will fill your mug from home for you if you ask and others will even give you a slight discount!
Remember that all these little things count, no matter what you think. Even if you can’t bring your own mug, at least recycle the paper sleeve that many places use.