I have a folder on my laptop labeled Weeds & Wildflowers, some of the plants I consider weeds (that I'd love to see disappear for good) while others I really enjoy and wish I could see them pop up more often. Since they are all plants, I upload photo's to the database whether I consider it a weed or a wildflower.
For instance:
Spanish Needles (Bidens pilosa) is an important source of food for butterflies and bees etc. but it can spread and take over here in Florida and many around these parts think of it as a weed.
Although I used to have a love/hate relationship regarding
Vinca (Catharanthus roseus) I've learned to live with them. The flowers are pretty and they are fairly easy to yank out when they pop up in sidewalk cracks and in the flower beds. I never planted them, they are gifts from the birds ... and I have seen mass plantings of them that are really gorgeous!
I have a neighbor who considers
Blue Toadflax (Nuttallanthus canadensis) to be a weed. I tell her that they are wildflowers but she doesn't like the look when they appear in her yard every March and says they look too messy and weedy.
Same for
Asiatic Dayflower (Commelina communis). It tends to spread through turf grass sometimes but to me it's kind of pretty. I even dug a bunch out of the lawn one time and potted it in a hanging basket ... very pretty but again, some consider it a noxious weed.
Another lawn weed here in Florida is
Doveweed (Murdannia nudiflora) but the dainty flowers are really pretty and it's another that I wouldn't mind having take over and replace the sod in my yard.