Color is a clue, but not a reliable one. With some fruits, you can tell they're ripe by their color. As the acidity changes, the green chlorophyll breaks down. Some fruits like bananas and apples have bright colors underneath the green chlorophyll layer; the colors show through as the chlorophyll disappears. Others, like tomatoes, make their red-orange compound at the same time that the chlorophyll breaks down. Bluish-red berries become a deeper, more intense red as they ripen. For these fruits—bananas, apples, tomatoes, red berries, cherries—color change is an excellent indication of ripeness.
Aroma hints strongly at flavor. Smell is especially important when color is not a good indicator of ripeness—for example, with most melons. Chemical changes take place in ripening fruits that cause them to produce sensuous, luscious-smelling volatile compounds. Sniff the blossom end of the fruit (the end opposite the stem) and only select fruit that has a full, fruity aroma.
Feel for a tender texture. As fruits ripen, the substances that hold the cells together (hemicelluloses and firm pectic substances) break down and convert to water-soluble pectins, which makes the fruit become softer and softer, so a gentle squeeze is a good test for ripeness. If a plum is rock hard, it isn't ripe. The squeeze test is especially useful with fruit that doesn't have a hard or thick rind, so squeeze stone fruit, pears, kiwis, and avocados. This doesn't work well with melons or pineapples, but even with these rough-coated fruits, a little give is a good sign.
Heavy is good. Weight can be a good indicator of ripe fruit. You'll often see the phrase "heavy for its size" as a positive attribute for fruit. It generally means that the fruit is at least fully mature, which is a good start on the road to ripeness. A heavy tomato or grapefruit, for example, is usually a good one.
If you have a grower nearby who allows you to pick your own or who's a conscientious producer who handles his produce well, by all means take advantage of that locally grown, just-picked ripe fruit. Your local county extension agent can help you find growers and farmers' markets. And speak up to the produce manager of your supermarket, too. Even big companies respond to consumer pressure.