Offline there are tons of local businesses which are known to be recession proof (ex: laundromats). What are some web equivalent verticals that would qualify?
Almost every industry takes a hit if the global economy tanks, but here are some verticals that might be more recession proof than others:
People always say "death and taxes" are things that nothing impacts, including the economy. Bring something to market in those two industries and the economy won't matter if it dips.
I would add babies and children. Along with pets, people have to spend money on their babies and children.