Both red (Trifolium pratense) and white (Trifolium repens) clovers seem to survive mowing pretty well, so they stick around from year to year in the yard. More so, the whites; reds tend to grow a little taller, so I usually only see the flowers in an overgrown edge of the yard.
Well, I do have to admit to transplanting one or two into a flowerbed where I can enjoy them throughout the growing season. Plus, they fix nitrogen from the air into nodules on their roots, so they're natural fertilizers for the other flowers!
Does that justify me transplanting "weeds" into the flower bed?
I guess I tend to side with A. A. Milne's Eeyore: "Weeds are flowers too, once you get to know them."