To keep my brick patio and walkways clear of sprouting plants, here's
what I've done with good success for the past three growing seasons.

Get a pre-emergent herbicide product called "Preen", or a similar one
from Miracle Grow. Sprinkle it on the brick and work it into the cracks
with a broom. You don't need a lot, Lightly water the brick.

Voila! you will have no unwanted sprouts for the remainder of the
growing season. It has really been worth it to me, since I have nearby
bird feeders which afford a good supply of seeds to sprout in the
cracks.

This won't work on grass which spreads via its roots. For that, I would
just pull out the interlopers. Roundup could also be used with the
previously mentioned cautions.

Good luck!
Tom