Thank you, Jean! Now I must go take another photo and ask a new question, because I've been removing something else all summer that I thought was henbit. :)

I don't know what this is but I'm certain it isn't Henbit (Lamium amplexicaule). Nor is it Lamium purpureum (Red dead nettle). It may be a Galeopsis, perhaps G bifida, but I don't know US species. Also we have no idea where this plant is growing.

I must agree that it's not Henbit - I am all too familiar with that; OP, where are you located?

Sorry, I'm in northern Vermont. An entire bed of this stuff appeared around a black cherry tree in our front yard this year, with a few scattered about in other parts of the yard. Those all had the purple flowers. We also have a few of what appears to be almost the same plant, but with white flowers, around the black cherry trees in the back yard, but they are not so densely packed. I will attach another photo that gives a wider perspective, from earlier in the season before they started to flower. They really look rather nice, but I'm concerned about how invasive they seem to be. Thanks so much for you help with this mystery!

After finding another plant in a different corner of the yard that was a bit farther along and had a series of flower balls on each stem rather than one, then doing some more googling, I'm leaning toward its being some kind of wild mint or maybe pennyroyal, which apparently is a type of mint in the UK version, but not in the US variety. Does that sound right?

Show us the plant with the flower balls, please.

The plant in your first photo isn't any kind of wild Mentha, including Pennyroyal. Apart from the appearance being wrong, absence of a smell is a clincher. It sounds to me as if you have various different plants in your yard in the family Lamiaceae but without pictures we can't tell you what they are. Can you show us all the plants?

Did you research the name I gave above?Galeopsis

Here's a photo of the flower balls. And no, I got distracted and totally forgot to research the Galeopsis, which now that I have looks as if that is exactly what it is (the bifida variety). And the other similar plant with the white flowers is probably another kind of Lamiaceae (mint family) as you suggested. Thanks so much for all your help, and especially for the link to that wonderful New England wildflower website!

It's really been rather pretty until just now, but being so invasive I suspect it would be wise to start trying to get rid of it. Would you all agree?

PS I think I may have got rid of all the white flower variety already (they're a bit uglier), but will take another look around this afternoon and send along a photo if I can find one.

Thanks again to all!