Coffee and plain tea, for one thing.
You can also order any milk-based drink made with soy milk instead of cow milk. It will cost you a little extra, but it's still pretty tasty.There are also iced tea drinks like the Passion Tea Lemonade (one of my favorites).
If in doubt, the Starbucks website can generally give you a good idea of what's in the various flavorings.
A quick word of warning, though — the Pumpkin Spice Latte is not vegan, even if made with soy milk. The syrup contains a small amount of nonfat milk powder.