I live in South central Indiana, US, and these have just started appearing in the grass in my yard. I just bought this house last fall so I've never seen them. Anyone know what they are? Are they harmful to dogs?
We called those "Indian strawberries". They are also known as Mock Strawberry (Duchesnea indica). Survivalists are pretty familiar with this plant.
They are a lot like strawberries in appearance, but the berry is rounder, not pointed, and held upright (they point up) on the stem, not pending. Though the berries are edible, they don't have much flavor at all. The leaves are also similar, and the flower is yellow, not white. The fruit's seeds are the same color as the fruit. They flower late spring and throughout summer. Your specimen looks like it was nibbled on at some point. The inside of this berry is white and kind of spongy and dry (especially compared to the real thing, i.e. wild strawberries.) The stalk it's on is hairy (as it should be) but damaged, and only one part of the leaflet is visible in your photograph.
They're in the Rose family, but there's some discussion about what genus they really belong to; may be more similar to Potentilla.