Four have flowers in racemes.These are all perennials.
Two are small (6" or so tall), found in grassy areas, with flowers in racemes:
Veronica officinalis, Common Speedwell
Thick, hairy leaves, up to 2" long.
Veronica serpyllifolia, Thyme-leaved Speedwell
Leaves less than an inch long.
Two are larger (up to 3' tall), found along streams (only in the Piedmont), with flowers in racemes:
Veronica anagallis-aquatica, Water Speedwell
Leaves are stalkless and may clasp the stem.
Veronica americana, American Speedwell
Leaves have short stalks.
A rare native plant.
Six have flowers that aren't in racemes. They grow from the junctions of the leaves and stem (the axils.)These are all annuals.
Two have flowers with no (or very short) stalks, and not in racemes:
Veronica arvensis, Corn Speedwell
A hairy plant with tiny blue flowers.
Veronica peregrina var. peregrina, Purslane Speedwell
A smooth plant with tiny white flowers.
Native.
Four have flowers with stalks, not in racemes:
Veronica hederifolia, Ivyleaf Speedwell
The plant is hairy, and the leaves are wider than long.
Veronica persica, Bird-eye Speedwell
Showy flowers about 1/2" wide on long stalks, above the leaves.
Veronica agrestis, Field Speedwell
Flowers about 1/4" wide; "mature calyx-lobes tapering, longer than the capsule; seeds 3-8 per cell of the capsule."
Veronica polita, Speedwell
Flowers about 1/4" wide; "mature calyx-lobes about as long as the capsule; seeds 9-12 per cell"
Piedmont only.
Sources: The Flora of Delaware, Herbaceous Plants of Maryland.