Do you throw out herbs and spices that are out of date?

It varies according not only to the type of herb and spice, but also to the type and quality of the original preparation, and how they're stored thereafter. Most can keep for years, stored in an airtight container in a dark, cool, temperature-stable place. With herbs, sprinkle a little into your hand and rub it between your fingers - it should activate the oils, and the aroma. If you can't smell much, they've had it. I've got big jars of thyme and rosemary that I very rarely use, but have been stored well, that both have a BBE of 2013, and they're still pungent and useful. Your mileage may vary.