Probably you don't want to read Madeleine Morgenstern's Greyhound gross-out report:
But I have to reply in some detail to a commenter who urged people to beware of receiving visits by anyone who's been in New York or New Jersey, because if these people carry German roaches or eggs with them, only a "full tent fumigation" will get rid of the pests.
Briefly, this commenter sounds like someone who's been exploited by an extermination service; as such s/he has my condolences. You don't have to spray anything or fumigate anything to get rid of German roaches. You just have to persevere.
Do you have German roaches or some other breed? German roaches are smaller, easier to look at, and harder to get rid of than American, Oriental, wood, or palmetto roaches, but species identification doesn't really matter; they're all vulnerable to the same safe, natural techniques. And those are:
(1) Clean and dry out your home. Roaches gnaw on wallpaper, carpeting, glue, fabric, and other things you wouldn't think of as food, up to and including damp wood, but they really love scraps, crumbs, and puddles of spilled food, especially junkfood. And they need plenty of water. You can't get rid of roaches just by maintaining a clean, dry home, but it's much easier to get rid of them if you start with a clean, dry home.
(2) Next, buy some borax, a natural mineral powder that also helps discourage mold and absorb odors, and kills other small vermin like ants and slugs. Borax crystals are hard and sharp; they irritate large animals on contact, and they kill tiny animals on contact, but they're not especially harmful to humans or pets. (Except to birds, who have been known to eat enough borax to make themselves sick; birds have died from eating large amounts of borax.) You can use 20 Mule Team washing soda straight from the box, or buy borax-based formulas in plastic applicator bottles. Apply a light coating of borax to the backs of kitchen cupboards, the floor below the sink, the baseboards in the kitchen and bathroom, and any other places where you find a lot of roaches. When you clean these areas, add fresh borax as necessary for six months after you last see a roach.
(3) Swatting the vermin is a small contribution to what can be a slow process, but every little bit helps. It can help if you live with an indoor cat who chases everything that runs across the floor.
(4) Another small contribution can be made by placing glue traps in areas of roach activity. Just check them and replace them when they're full; if you trap a pregnant female who drops the egg in the trap, you'll actually be breeding roaches in an old trap.
(5) Keep this up until you don't see them any more. That's all it takes...but usually it takes a few months. If the vermin are in an apartment building, and you move, repeat the treatment in your new home just in case you've inadvertently brought in bugs.