Growing up, we never had dumplings on Lunar [for me, Chinese] New Year, but we definitely ate a dish called jai (Buddha's delight) as the first meal of the new year. My mom would also make this sweet soup-y dish that was basically mochi in a sweet brown sugar syrup for dessert. This year, I'm just making jai with cellophane noodles, yuba, seitan, shiitake mushrooms, and some greens. And dumplings for sure.
Koreans usually have tteokguk for the new year (there's a good vegan recipe here
) and banh chung is a must for the Vietnamese new year (mel c has a recipe on her blog
, but it's a pretty labor intensive dish).