From wikipedia:
I was told that the belief was due to the coloring of black-eyed peas protecting one from the evil eye. It was a Voodoo thing and beneath our civilized observance. It just so happened that we had ham for dinner every year on New Year’s day, and black-eyed peas go really well with ham, that’s all. 
And, coincidentally, I made ham and sweet-potatoes for dinner yesterday. There was also a veggie mix with a few black-eyed peas hidden in it, because one of us really doesn’t like them much. Evil-eye protection is in place for the year. 
New Years day breakfast is always home made cinnamon buns. Dinner is always risotto. This year was champagne risotto with lemon and peas.
A simplified New England boiled dinner; a corned beef brisket I started curing a week ago with Morton Quick Cure, coriander seed, black peppercorns and bay leaf, simmered for hours with garlic, bay, black peppercorns and coriander seed, and then finished with potatoes, carrots, onions and cabbage. After a couple of days of boiled dinner we’ll have reubens and cold corned beef sandwiches with brown mustard, and when we’re tired of it all the leftovers get ground up and baked into corned beef hash.
Ham, cornbread, collard greens and blackeyed peas (that we grew ourselves and dried).
I didn’t eat any dinner, because we had lox and bagels for brunch-ish, and I wasn’t hungry later. Just had a bowl of McConnell’s Sweet Cream ice cream with Williams-Sonoma Salted Caramel sauce (the only jarred sauce I’ve found that’s worth eating).
When I was a kid, New Year’s Day was when my mom had to have dinner for the extended family. Apparently it was a tradition with my dad’s family (Italian) to have a big family meal. Since my dad’s brother and his wife hosted Christmas Eve, my mom got stuck with New Years Day. She hated it. After being up late the night before, it was the last thing she wanted to do. But she did it. She always made a beef roast and a pork roast with potatoes, carrots, etc. My grandma would also bring the soup (which is now called Italian Wedding Soup) we just knew it as meatball soup!
After my grandparents and dad died, that meal went by the wayside. Now my husband and I usually get a pizza.
Black-eyed peas baked in casserole with chopped sautéed bacon, ham, scallion, garlic, rice, and chicken stock. Dash of vinegar.
Gombo z’herbes, which is basically a mess o’ greens flavored with scallion, garlic, and herbs. And more vinegar.