As Tom points out a weed is any plant that is growing in a place it is not supposed to be. If I have a tomato plant growing in with my lettuce, it is a weed. Dandelions at one point in time were a food crop, they were imported from Europe, and then went wild.
When they grow out of control in my yard? Yes, they are weeds. I did just read an article that their roots have some great cancer fighting properties to the though. So maybe I need to cultivate them instead.