I recently did a couple of weeks of traveling. Over the years, I've learned to pack lighter and lighter, so on this trip, I brought only one kind of shirt: The REI Sahara Tech Tee. The tech tees are 100% polyester, but they feel as comfortable as cotton. They breath very well, and amazingly, keep you cool in hot climates and warm in cool climates. They don't wrinkle, and the polyester material means that they don't stain or stink. And they are so lightweight that you can roll up an extra in your day bag for sudden climate changes or spur-of-the-moment dining at a "long sleeve" restaurant.
I brought six of them, three short sleeves and three long sleeves, all black. For $25 each, they are an excellent bargain.
