based on your preference, it could be either.
looks like wild violet to me, which can take over if you let it.

Is it a vine or ground cover? How does it propagate itself? Does it flower and when?

It looks like a violet to me as well. I believe it would be classified as a ground cover. My lawn has loads of lawn violets that pop up every year, and show up in my beds as well. I'd assume they're seed propagated, considering the mass and how they show up everywhere, even in my window boxes. Personally, I love them in the lawn. They're only a problem in the furthest part of my yard, and it looks gorgeous from the deck. In DH's eyes, it's a weed that should be destroyed. He has yet to find something that works ;)

If you are interested in having some patches of weed free lawn, this is a problem for you. Otherwise, many people really enjoy it.

I USED to think it was lovely.

Thanks, Rhizo. I have no problem with a weedy lawn, as long as it's all green and there isn't anything prickly in there. I'm certain there is more clover etc. than grass! I just don't care for bare spots, which I'm working on now, going through the watering new seed routine. I had a landscaper look at it and he suggested starting over--killing the lawn and reseeding the whole thing or putting in sod. I don't care that much, plus my priorities on "this old house" are more on the interior, not to mention the expense and mess. The landscaping just needs to be presentable so I don't look like the trashiest house on the street. :) I've planted a few perennials this year, and have beautiful azaleas all around the house that just need a little tlc and shaping. It'll take a couple (few!) years, but I think it'll look great with a little planning and pruning.