My friend recently sent me a link on "the absolute best way to store green onions." Instead of putting bagged scallions in the crisper bin or vegetable drawer of a frigid and dark refrigerator, store them near a sunny window in a transparent glass of water (and change the water once it gets cloudy). To test this method of storage, I left some scallions in the fridge (on the right) and stuck the rest in a glass mason jar filled with tap water (on the left). The results were impressive.
It looks like an overgrown jungle in there! There was at least an inch of growth on the scallions that were partially submerged in water. Also, as you can visibly notice, the onions from the fridge were flaccid and droopy (and yellowed, but I cut those parts off). According to the link, the scallions will grow indefinitely (you are supposed to only use the verdant tops by snipping off what you need, and not the white portions), but I haven't tested this yet. And I have to admit, I'm a little suspicious about how the scallions would continue to grow without the nutrients from soil, but I'll let you know how this experiment goes!
Update: A fellow food blogger informed me (in the comments below) that after three (3) to four (4) weeks, the roots will begin to rot. But she gave her seal of approval to this method for short-term scallion storage! I should note that when I changed the water, I made sure to thoroughly rinse and scrub away the oniony slime on the bottom of the scallions. I also peeled back the visibly brown and wilted layers at the bottom that had been soaking in the water. It is a little gross, but I believe it helps the green onions keep their "shelf-life" longer. I also noticed the green parts of the scallions bent pretty easily (they do not seem very fibrous).