A combination of vinegar and baking soda can unclog drains without using chemicals. The fizzing reaction of the two ingredients can be helpful in dissolving grime buildup in the drain. Depending on the sink and pipes, however, the results may vary.
To use this solution, measure 1/2 cup baking soda and pour it down the drain. Follow this up by pouring 1/2 cup of vinegar into the drain. The mixture fizzes and dissipates. When the mixture settles, flush the drain with hot water and let it sit for an hour.
Using a bent wire hanger to dislodge clogs can also be effective to clear a drain.