The moth at the top of this post appears to be a Boxwood Leaftier (Galasa nigrinodis) in the family Pyralidae. The primary known host plants for this species are boxwoods (Buxus sp.), which are not native to North America. Presumably it evolved to feed on a native plant, but so far that plant's identity is unknown. Despite its bright red and white coloration, this moth proved to be more difficult to identify than I expected, mainly because I was looking for it in the wrong families. Luckily, one of my Flickr contacts set me straight.
The second moth is a Yellow-fringed Dolichomia (Dolichomia olinalis), also in Pyralidae. Larvae of this species feed on oaks, of which there are plenty in my neighborhood. This was another moth that I had trouble figuring out until I came across a Flickr contact's photos of the same species. It seems that the yellow triangles at the leading edges of the forewings distinguish it from similar species.