If not stored properly scallions can turn quickly. Fortunately, storing them is a snap. Fill a jar with about an inch of water. Put your scallions (with roots) in the jar. Cover with a plastic bag or plastic wrap and pop in the refrigerator. Change the water once every day or two.
Also, scallions freeze quite well. Wash them off, chop them up, and put them in your freezer! They'll last for quite a while.