Fill a tea kettle with water and bring it to a boil on the stove. Immediately pour the boiling water over the weeds appearing in the basement cracks. The weeds should exhibit signs of dying with a few hours; however, if necessary, repeat the process. The plants should die within 24 hours; don protective gloves and throw them away in a plastic bag that can be sealed. If the weeds appear to be going to seed, remove them from the cracks gently, so as to avoid spreading any further seeds around.
Wait for the hot water to dry, and then sweep the area to remove any dried plant debris. Fill a bucket with hot water and an all-purpose household detergent or bleach -- which will disinfect the floor, as well. Use a stiff-bristled brush to scrub the crack and the floor on both sides of the crack. Wash the entire area to remove any plant residue or seeds from the floor that could dry and fall back into the cracks. Rinse the area thoroughly and allow it to dry; placing several fans in the basement will help circulate the air and completely dry the floor and interior of the crack.
Cracks can be filled with hydraulic concrete, but may reappear as the house shifts. For larger cracks, homeowners can purchase a foundation crack repair kit, or hire a contractor to fill the crack with a commercial polymer foam or epoxy. Follow the manufacturer's instructions on how to properly dry the filler. Once the prescribed time has passed, seal the basement floor with a concrete sealer, which repels water, water vapor and underground gasses. Sealers can also be purchased at home repair stores and easily applied with a mop, roller or brush.
Keeping the basement air dry may be the most important process in prohibiting the return of unwanted plant life. A dehumidifier pulls air through a filtering process, removing water from the air and expelling dry air back into the basement. For an average investment of $200 for the appliance, homeowners can breathe easier knowing that the humid conditions that make the cracks in to floor hospitable to plant life are being rectified. Large basements may require more than one, and keeping the moisture-collection pan emptied out and replaced is important. Running additional fans in the basement--especially an unfinished area--for air circulation will also work to keep the basement dry; fans can also be used in conjunction with a dehumidifier for larger basements.