NEVER STORE YOUR FRUIT IN PLASTIC BAGS!
Sweet red cherries: Depth of color is more important than the particular shade of red. Look for fruits with deep, dark saturation. If the stem is intact, a bright green color indicates freshness; however, a lack of stem doesn't necessary mean the cherries are low quality. Red cherries should also be firm. Wrinkling along the shoulders near the stem means the cherries have sat at room temperature; they may still be sweet, but are probably not at peak freshness.
Rainier cherries: Many people think these reddish-yellow cherries (photo below) are underripe, but this is the natural color of Rainier cherries. They are also naturally less firm than red cherries. A red or pink blush indicates sun exposure, which leads to sugar accumulation. Brown flecks are generally not defects but a further indicator of sugar accumulation. (Red cherries have this, too, but it's less visible.)
How To Store
Cold storage is key to keeping cherries fresh. According to a cherry expert we spoke to, cherries can lose more quality in one hour at room temperature than a day in the refrigerator. Thus, get your cherries in the fridge as soon as possible.
Wash them with cold water just before eating. Avoid washing prior to storage, as moisture can be absorbed where the stem meets the fruit and lead to splits or spoilage.
Cherries can also be frozen. Pit them if you wish, or keep them whole with stems intact. Spread them in a single layer on a baking sheet, freeze until firm, and then place in a bag or container.