So many regular series, since the dawn of time, have had Christmas episodes, which I don't consider "specials." Still, I suppose I might as well at least list some of them, in passing. At least the ones I personally remember (even vaguely) seeing; surely there have been many I've seen that I've forgotten, and many more that I've never seen at all. Also note that some shows, particularly animated ones, have episodes broken into separate shorts, not all of which will necessarily be related to the holiday. (This section is for not only Christmas, but potentially Hanukkah or any other wintery/December holidays, including fake ones.) 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.
= My favorite Christmas episodes. (Some eps that I don't remember well might become favorites if I ever see them again.)
Martin Mystery
Season 1: Eternal Christmas (IMDb)
The Mask
Season 1: Santa Mask (Christmas Specials Wiki; IMDb; Wikia)
The Mayor
Season 1: Grey Christmas (Amazon; IMDb)
Men in Black: The Series
Season 2: The Black Christmas Syndrome (Christmas Specials Wiki; IMDb; Wikia)
Metalocalypse
Season 3: Dethmas (Christmas Specials Wiki; IMDb; TV Tropes; Wikia)
The Michael J. Fox Show
Season 1: Christmas (Amazon; A.V. Club; IMDb)
Mixed-ish
Season 1: Do They Know It's Christmas? (Amazon; Black-ish Wiki; Christmas Specials Wiki; Hulu; IMDb)
Modern Family
Season 1: Undeck the Halls (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; Wikia; Wikipedia)
Season 3: Express Christmas (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; Wikia; Wikipedia)
Season 5: The Old Man & the Tree (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; Wikia; Wikipedia)
Season 7: White Christmas (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; Wikia)
Season 10: Stuck in a Moment (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; TV Tropes; Wikia)
Season 11: The Last Christmas (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; Wikia)
Monk
Season 6: Mr. Monk and the Man Who Shot Santa Claus (Amazon; Christmas Specials Wiki; IMDb; TV Tropes; Wikia; Wikipedia)
There have been other Christmas eps, but I don't quite remember them.
Moral Orel
Season 1: The Best Christmas Ever (Christmas Specials Wiki; IMDb; Wikia)
Mr Bean
Series 1 (I think): Merry Christmas, Mr Bean (Christmas Specials Wiki; IMDb; Wikia; Wikipedia; YouTube)
Muppet Moments
Season 1: Ho Ho Ho! (YouTube); Christmas (YouTube); Santa Claus (YouTube)
The Muppets
Season 1: Single All the Way (Amazon; A.V. Club; IMDb; Wikia)
My Life as a Teenage Robot
Season 2: A Robot for All Seasons (Amazon; Christmas Specials Wiki; IMDb; Wikia)
My Little Pony: Friendship Is Magic
Season 2: Hearth's Warming Eve (Amazon; Christmas Specials Wiki; IMDb; TV Tropes; Wikia) Set on a Christmas-like holiday.
Season 5: Hearthbreakers (Amazon; Christmas Specials Wiki; IMDb; TV Tropes; Wikia)
Season 6: A Hearth's Warming Tail (Amazon; Christmas Specials Wiki; IMDb; TV Tropes; Wikia; Wikipedia)
Season 8: The Hearth's Warming Club (Amazon; Christmas Specials Wiki; IMDb; TV Tropes; Wikia)
Standalone special: Best Gift Ever
My So-Called Life
Season 1: So-Called Angels (Amazon; A.V. Club; IMDb; This Was Television; Wikia)
The Neighbors
Season 1: Merry Crap-mas (Amazon; IMDb; Wikia)
Season 2: A Christmas Story (Amazon; A.V. Club; IMDb)
New Girl
Season 1: The 23rd (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; Wikia)
Season 2: Santa (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; Wikia)
Season 4: LAXmas (Amazon; A.V. Club; IMDb; Wikia)
Season 6: Christmas Eve Eve (Amazon; A.V. Club; IMDb; Wikia)
The O.C.
Season 1: The Best Chrismukkah Ever (Amazon; IMDb; TV Tropes; Wikia)
Season 2: The Chrismukkah That Almost Wasn't (Amazon; IMDb; Wikia)
Season 3: The Chrismukkah Bar-Mitzvahkkah (Amazon; IMDb; Wikia)
Season 4: The Chrismukk-huh? (Amazon; IMDb; Wikia)
Odd Squad
Season 1: Reindeer Games (Amazon; IMDb; Wikia)
Parenthood
Season 4: What To My Wondering Eyes (Amazon; A.V. Club; IMDb; NBC)
Phineas and Ferb
Season 2: Phineas and Ferb Christmas Vacation
Season 3: A Phineas and Ferb Family Christmas (Disney+; IMDb; TV Tropes; Wikia)
Picket Fences
Season 1: High Tidings (Amazon; IMDb)
Season 2: Blue Christmas (IMDb)
Season 3: Away in the Manger (IMDb) This was almost a crossover with The X-Files
The Pretender
Season 1: Not Even a Mouse (Amazon; IMDb; Wikia)
Psych
Season 2: Gus's Dad May Have Killed an Old Guy (Amazon; IMDb; Wikia)
Season 3: Christmas Joy (Amazon; IMDb; Wikia)
Season 5: The Polarizing Express (Amazon; IMDb; Wikia)
Pucca
Season 1: Tis the Season for Revenge/Northern Lights Out/Secret Santa (Amazon; Wikia)
Quantum Leap
Season 3: A Little Miracle (Christmas Specials Wiki; IMDb; NBC; Wikia)
The Real O'Neals
Season 2: The Real Christmas (Amazon; IMDb; Wikia)
Rick and Morty
Season 1: Anatomy Park (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; TV Tropes; Wikia; Wikipedia)
Season 4: Rattlestar Ricklactica (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; TV Tropes; Wikia; Wikipedia)
Rock Lee & His Ninja Pals
Season 1: Christmas Is the Last Chance for Love! (IMDb; Wikia) (one segment; second is about New Year's)
Roswell
Season 2: A Roswell Christmas Carol (Amazon; IMDb; Wikia)