Like carpet, laying down newspaper will block sunlight, prevent oxygen from reaching the soil and smother weeds that are already growing. Put down 10 layers of newspapers on the soil, wet it with water to hold it in place and then cover with mulch.
Bring a solution of about 1 cup salt in 2 cups water to a boil. Pour directly on the weeds in the cracks of your path to kill them. Another equally effective method is to spread salt directly onto the weeds or unwanted grass that come up between bricks. Wait for rain to rinse it off.
Those old shower curtains will also come in handy next time you do any landscaping with gravel or bark chips. Just place the shower curtain under the mulching material to prevent annoying weeds from poking through. While weeds can be pests, bugs can be beneficial.