A number of shows have had New Year's Eve/Day episodes, though they're not quite as common as episodes centered around other holidays. But whatever, I'll make a list of any that I can remember having seen (or have probably seen, even if I don't remember it). Oh, and while the holiday may play a particularly prominent role in many of the episodes listed here, sometimes it's only a very minor aspect of the episode's plot.

30 Rock
Season 4: Klaus and Greta (Amazon; A.V. Club; Hulu; IMDb; Wikipedia)

Babylon 5
Season 1: Chrysalis (Amazon; A.V. Club; IMDb; TV Tropes; Wikia; Wikipedia)

Friends
Season 1: The One with the Monkey (Amazon; A.V. Club; IMDb; TV Tropes; Wikia)
Season 5: The One with All the Resolutions (Amazon; IMDb; TV Tropes; Wikia)

Futurama
Season 1: Space Pilot 3000 (Amazon; A.V. Club; IMDb; Infosphere; TV Tropes; Wikia; Wikipedia)

Girl Meets World
Season 2: Girl Meets the New Year (Amazon; Disney+; IMDb; Wikia)

How I Met Your Mother
Season 1: The Limo (Amazon; Hulu; IMDb; TV Tropes; Wikia; Wikipedia)
Season 7: Tailgate (Amazon; A.V. Club; Hulu; IMDb; TV Tropes; Wikia; Wikipedia)

Modern Family
Season 4: New Year's Eve (Amazon; A.V. Club; IMDb; Wikia; Wikipedia)

Murphy Brown
Season 2: What Are You Doing New Year's Eve? (IMDb; Wikia)
Season 11: Happy New Year (Amazon; IMDb; Wikia)

The O.C.
Season 1: The Countdown (Amazon; Hulu; IMDb; TV Tropes; Wikia)

Phineas and Ferb
Season 4: Happy New Year! (Amazon; Disney+; IMDb; OHS Wiki; TV Tropes; Wikia)