Seems like a simple enough question doesn't it? On one of my first days of hort school a few years ago the professor posed this question to the class. The whole class sat there dumbfounded. Some brave soul finally raised their hand and starting listing off various "weeds"; crabgrass, clover etc. The professor instantly shot it down and said that he wanted, "the botanical definition of a weed." We were all stumped.
So it's a bit of trick question (Thanks Professor Mike) because the botanical definition of a weed is any plant that you don't want in that place. Kinda crazy, no? So that old yew you hate that's been in front of your house for 30 years and looks like crap because it's never been pruned or been pruned the wrong way, it's a weed so get rid of it!
There are some plants that we commonly associate as weeds like creeping charlie, mugwort, purslane and many more. The one pictured above has been growing in my yard for years, and I leave it, because to me it's just not a weed. It's common name is Jewel weed, which if a home gardener would identify it would probably cause them to rip it out. I leave it, because I think it's pretty, and the flower color goes nicely with my back woodland garden. It also happens to be an antidote for poison ivy exposure. It won't help you once you get the rash, but if you touch some poison ivy while working it the garden you can crush up the jewel weed and get some of the oil off before it sets in and you are in agony. The best thing about jewel weed however, is it generally grows close by poison ivy. That's one smart plant. So since the jewel weed seemed to be spreading in my back garden I went on a little hunting mission, and guess what? ugh.