I keep garlic in a garlic crock (on the counter at the farm) or in a hanging basket. The quality of garlic one buys makes a difference. Garlic that has a "purplish" color on the skin is fresh garlic (garlic is usually cured for 2 weeks). The variety of garlic also makes a difference. There are varieties that are "keepers" (when the stem dries, it is a hard stem--Georgie Boy is one such variety, as is Russian Red) and those varieties that don't have the hard stem when dried--these varieties do not keep as long. Properly dried, garlic can last up to a year without drying up. Not that it would ever last that long in my house--I use a lot of garlic--probably 3-4 heads / week.
IME, garlic from California, local (+1), and Argentina lasts a lot longer than garlic from China. I have grown garlic, but didn't know when to cut the greens back, so did not get my garlic to bulb. Hopefully, the garlic we plant in October will produce nice bulbs next summer.
Never store onions with potatoes. Keep potatoes in a cool, dark spot in a burlap bag or paper bag. We cure the potatoes we dig in the fall in the sun for at least a day, then we let the potatoes sit on screens for another week, put in burlap sacks and store in a cool, dry place. They start to sprout about February.
We also store carrots and beets in sawdust (since we have a saw mill) and store those in the cold room in the basement. We have beets and carrots until the spring. The worst thing that happens is the carrots start sprouting tops towards spring. But, carrots do last a long time in the crisper.
If you keep zucchini in a cool, dry, dark place, they can keep for 3 weeks or longer. A friend begs me for a "baseball" bat zucchini in September and uses it when she makes her mince pie mix after Canadian Thanksgiving. I try to process the zucchini and freeze it, so I can't swear to it keeping that long, but that is what she does.
I wash romaine lettuce, spin it dry, and wrap in a clean dish towel. This seems to keep it fresh longer than other methods.
I never put tomatoes in the fridge--doing so, causes the tomatoes to lose flavor. Tomatoes are delicate--when refrigerated, the membrane breaks down and the tomatoes develop a mealy texture. If you do store them in the fridge, don't store for more than 1-3 days. Take them out 24 hours before eating and let sit on the counter at room temperature. Some of the enzymes will re-activate. (Here's an interesting article on how to select retail tomatoes, etc.).
