This is a new-to-me weed, even though it's growing all around Robbins Hall where I've been working since typewriter times. Fumitory (Fumaria spp.) is a lacy, vine-like annual native to Europe. Looks sort of like parsley, though it's not related. It doesn't have tendrils, but it has 'grabby' foliage, and it drapes over other plants and fences by coiling its stem ends. Fumitory is in the poppy family (Papaveraceae). Its flowers are small, white to purplish, and bilateral in axillary racemes.
I figured out what this was by using this weed ID tool available through the Weed Research & Information Center.
