According to Japanese belief, what you dream on the night of January 2 will decide your fortune for the rest of the year. That first dream of the year is called hatsuyume.
Hatsuyume.net explains:
"Since New Year's Day is a day for quiet celebration, and people don't start returning to their daily routines until the second day, the hatsuyume is usually the dream you have on the night of January 2. The best dreams are said to include Mount Fuji, hawks or eggplants, probably because they deal with great heights -- Fujisan because it's the tallest mountain, hawks because they fly high in the air, and eggplant because its price used to be very expensive."

I believe I dream every night. Often my dreams are vivid and detailed. I know I dreamt last night, but I can't remember it at all. Maybe it's better that way. Would rather not know what's in store.