About 13 or 14 years ago my wife and I flew SFO-EWR on a red-eye departing on December 31. We crossed into the Mountain time zone around 11:30 pm, and so we had no proper NYE. I don't recall any announcement being made; what was more memorable is that it was a Continental Micronesia DC-10.
Today, on a live TV-equipped 738 or 739, I suppose one could watch Dick Clark live.