We have all at one time or another bought a partly green banana or a too-firm tomato, knowing they would ripen up in a few days and be ready to eat. Can you count on this ripening process for all fruits? No - a lot of them, but not all. Besides bananas and tomatoes, the more common ones that do ripen after picking include apricots, papaya, avocados, mangoes, peaches, pears, plums, and kiwis. You will not see ripening for berries, cherries, pomegranates, grapes, or citrus fruit.
Melons, apples, and pineapple are sort of in between; they will soften once picked but will not get any sweeter.