For an area where you don't want to grow anything, salt works great. Dump it in the cracks and leave it, the rain will wash it through and away. Some say that salt can make and area sterile for up to 3 years. It does this by killing the biology in the soil.
If you're talking about gardens for flower beds, vinegar works good.
Let's not forget good old hand-pulling and shovel-disking. It's a bit of work, but it's also one of the surest ways to get rid of the grass