Brooke here:
When ripping up the earth for the Vestigial Lawn, I kept finding scraps of some sort of tile. Here are three of the largest pieces:
These differ from brick, obviously, and my best guess is that someone disposed of a pile of … somethings. I originally thought these might have come from an old patio but if they did the patio was either very small or someone had hauled almost all of the tiles away when it was abandoned: these scraps were everywhere but there were only enough of them for five wheelbarrow loads. Since there is no practical use for a tiny patio and I’m darned positive no one has bothered to haul off any waste materials on this property, ever, these fragments must have been junked.
The underside (A) has a lip and the top (B) has a series of ridges (I’m just guessing here. The top and bottom could also be reversed). The edges are rounded but what’s left of them looks square. What are these? My best guess is interlocking roof tiles but these seem really impractical for a roof.
Flying by night 
Piece #B looks like it could almost be a decorative baseboard, bottom edge to the left. Or could they have been used upright to edge a flowerbed or something?
The ridges look like the underside of Spanish roof tiles, like for the hacienda style homes we have down here in Florida. But I can’t see the other side on the photos very well. Are they curved slightly and smooth to the touch?
I agree that they look like some kind of overlapping roof tile, probably more than a garden edger. They at least don’t look like any kind of pot that I’m familiar with, neither the round or square pot varieties. Maybe used for edging the roof of a patio, as much of a bad design move as that seems? Five wheelbarrow loads seems like a lot…
As an aside, I love the A Girl and her Fed ‘Future Member of Ben Franklin’s Undead Pixie Army’ pin, and would be ecstatic if it came on a shirt or a hoodie. I’d buy like, three.
Looks like structural terra cotta to me. Structural terra cotta isn’t bricks, but more honey-combed (generally) forms used from linings to entire buildings. You may have had a small outbuilding or addition built from it, or perhaps it was used for a flue liner. Here’s linkage to an online piece that clearly shows the same stuff as what you have: http://historicbldgs.com/terra_cotta.htm
looks like fossilized brownies to me. I bet all those weird shapes and scrollwork are from some funky shaping for a fancy cake.
I’d say roof tile. But considerign the rest of the property it might also be the remnants of an old atomic bunker…
I’m inclined to agree with the structural tile guess, but I’d bet it used to be some sort of drainage. Yes, they would be a horrible option to use for French drains or something similar.