This is a matter of personal preference. Some people like having them touch the floor since it creates a more luxurious vibe, while others don't like this since they can get in the way of furniture. If you're worried about tripping over your drapes or getting dirt on them when you walk across them, then try getting ones that are made from sheers so that they won't touch the floor all that much, if at all.
You should try to match your window treatment to other items in your home's interior design theme. For example, if you have wooden floors and wood accents up against your walls then solid-colored velvet curtains might not look as good as something with a floral pattern (unless you want an eclectic style).