Here's a thread to collect hints for choosing the best items of fresh produce - beyond the obvious things like wilting and size. Please add your own expertise.
RED DELICIOUS APPLES - Usually, they are anything but. In a pommology book, I read that for the sweetest, non-mealy ones, avoid the ones that are very dark red all over. Look for striations in the color, the overall apple being no darker than the darker of the red bars on the CH banner.
CARROTS - Avoid thick ones with cracks, as they will most likely be woody and bitter.
CITRUS - Choose pieces that are heavy for their size, to get the juiciest ones. For thinnest skins, choose pieces that are shiny, and with smoother skins rather than those with more distinct pores.
PINEAPPLE - If other people have already been plucking center leaves, that test is useless. Look for the ones with the greatest pinkish blush. A ripe pineapple has a heady, sweet aroma when you sniff the stem end. If it only smells slightly, keep it at room temp until the aroma develops.
TOMATO - To ripen tomatoes, keep them at room temp, stem end DOWN.
PEACHES and PEARS - They say these just soften after picking, but don't ripen further. I don't think that's true. Heavy fruit is the juiciest. Really hard ones won't ever get sweeter. Look for pieces that are slightly tender, with a blush, and keep them at room temperature until the aroma intensifies.
CANTALOUPE - A ripe cantaloupe has a slightly pinkish blush. Shaking it tells you nothing about sweetness. The stem end should smell fragrant. Pick the ripest looking one you can find, and leave it on the counter if it doesn't already smell ripe.
HONEYDEW - Same sniffing, shaking, and ripening as above, but look for the raised webbing of lines - called "sugar lines" - a yellow blush, and a slightly tacky feel, as if rosin had been rubbed on the skin. Finish ripening on the counter.
GRANNY SMITH APPLES - If you like them very tart and very crisp, pick shiny dark green ones with lots of white freckles.
SWEET RED ONIONS - According to a greengrocer I spoke with, look for squat ones with flat ends.
BING CHERRIES - The sweetest ones are shiny, dark, and - surprisingly - hard.
PLUMS - Should have some give when gentle pressure is applied, and have a slightly tacky, whitish "rosin" on the skin.
THOMPSON SEEDLESS GRAPES - Choose bunches that have a slightly golden tinge.
STRAWBERRIES - They get redder after picking, but not sweeter. They should smell intensely sweet. Avoid ones with white shoulders, as they have little flavor.