My own onions, taking matters into their own hands after being ignored for a while.
Thankfully, OrganicGardening.com compiled a list of the top 11 longest-lasting types of produce and how to keep them fresh. Here's the rundown (click on the address link to see more details and tips):
1. Apples: they can last for weeks sealed in a bag in the crisper drawer of your fridge.
2. Beets: remove the stems and they can last 2-4 months in your fridge.
3. Cabbage: they can last up to 2 months wrapped in plastic in the fridge.
4. Carrots: keep them as dry as possible by putting paper towel in their bag, and they can last several weeks to a couple of months.
5. Celeriac: as long as you keep it moist (or wrapped to preserve its own moisture) and in the fridge, it will last a couple of weeks, even after being cut.
6. Garlic: it will last the longest in a dark kitchen cabinet or in a brown paper bag in the fridge.
7. Onions: keep in a cool, dark location in a mesh bag and they can last for up to a month or longer.
8. Potatoes: they will last usually between 2-4 months in a cool, dark location, like in a basement cabinet.
9. Winter Radishes: remove the greens and store them like you would carrots and they'll last for about a month.
10. Winter Squash (Pumpkins, Butternut, etc): these can last for 2-6 months when kept in a dark place.
11. Rutabagas: store them as you would celeriac and they'll last several weeks.
Of course, as the website also recommends, you can also opt for frozen veggies, which are frozen within hours of being picked (so they are always fresh!) and will never go bad. :)