Black Eyed Peas
One of the most common here in America is the tradition of eating black eyed peas. Their shape is said to resemble coins, and because dried beans can be stored and then either eaten or replanted, their very nature echoes the idea of plenitude.
Black eyed peas are often eaten on New Year's in a Southern dish called Hoppin' John. This is basically a casserole of black eyed peas and rice, along with ham hocks and some seasonings. Emeril Lagasse has an excellent Hoppin' John recipe here on the Food Network website.
Another Southern America tradition, greens are eaten because they look like folded (American) money. Although now that our money is getting so colorful, that's not as true as it used to be! Collard greens and kale, in addition to being supercharged with nutrition, are easily available fresh this time of year. In the days before global produce transport, this alone was enough to recommend them!
My favorite kale recipe (and I do have one) is to make "kale crisps." Preheat your oven to 475. Mix cleaned kale leaves with kosher salt. Lay the leaves out on a cookie sheet and bake for 15-20 minutes, or until crispy. You won't believe it's kale!
The tradition of ensuring prosperity by eating golden food technically belongs to Chinese New Year, which occurs in February. But why not have some golden food on January 1st? A "golden" theme could include foods as diverse as fried tofu, sesame noodles, Ritz crackers, Lay's potato chips, and snickerdoodles.
Pork is considered a lucky food in many cultures. Pork indicates abundance and good fortune, not least because it proves that you had a pig to slaughter! Pigs are also considered lucky in Austria and other Germanic cultures because pigs always root forward. Animals which move backwards (like chickens, which move backwards when they scratch for food, or shrimps) are considered unlucky.
A ham hock is a classic addition to Hoppin John. Ham can also be served at the table as a main dish, or cooked with lentils in a pea soup (an Italian New Years tradition).
Herring is a popular New Years meal because they are an abundant fish, and their scales are silvery (like coins). Pickled herring is eaten at the stroke of midnight in many Polish and Polish-American homes.
In some parts of Spain, celebrants rush to eat twelve grapes before the clock finishes striking twelve. They are called "the Twelve Grapes," and are said to grant luck to anyone who can eat one at each toll of the bell. (Choking hazard!)
Sauerkraut is another classic New Years recipe, both because the leaves of the cabbage resemble money, and because sauerkraut is an abundant food. (If you have ever made sauerkraut, you know what I'm talking about!) The Pennsylvania Dutch are particularly fond of this tradition, and serve their sauerkraut with beef spare ribs.