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.)
3rd Rock from the Sun
Season 2: Jolly Old St. Dick (Amazon; Christmas Specials Wiki; IMDb)
30 Rock
This show has had several Christmas episodes, and I'm sure I enjoyed them all when they first aired, but I am shocked to discover that now I don't specifically remember any of them. Someday I expect I'll rewatch the series, and then I'll list those episodes here.
Aliens in America
Season 1: Church (IMDb)
Ally McBeal
I don't specifically remember any of this show's Christmas episodes, but I do have a Christmas CD from the show.
American Horror Story
Season 2: Unholy Night (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; TV Tropes; Wikia; Wikipedia)
American Housewife
Season 1: Krampus Katie (Amazon; Christmas Specials Wiki; IMDb; Wikia)
Season 2: Blue Christmas (Amazon; Christmas Specials Wiki; IMDb; Wikia)
Season 3: Saving Christmas (Amazon; Christmas Specials Wiki; IMDb; Wikia)
Season 4: The Bromance Before Christmas (Amazon; Christmas Specials Wiki; IMDb; Wikia)
Aqua Teen Hunger Force
Season 1: Cybernetic Ghost of Christmas Past from the Future (Amazon; IMDb; Wikia)
Aquarius
Season 1: Why? (Amazon; IMDb)
Arrow
Season 1: Year's End (Amazon; A.V. Club; IMDb; TV Tropes; Wikia)
Season 2: Three Ghosts (Amazon; A.V. Club; IMDb; TV Tropes; Wikia)
Season 3: The Climb (Amazon; A.V. Club; IMDb; TV Tropes; Wikia)
Season 4: Dark Waters (Amazon; A.V. Club; IMDb; TV Tropes; Wikia)
Batman: The Animated Series / The New Batman Adventures
Season 1: Christmas with the Joker (Amazon; A.V. Club; Christmas Specials Wiki; DCAU Wiki; IMDb; TV Tropes; Wikipedia; World's Finest)
TNBA Season 1: Holiday Knights (Amazon; A.V. Club; Christmas Specials Wiki; DCAU Wiki; IMDb; TV Tropes; World's Finest)
Becker
Season 2: Santa on Ice (Christmas Specials Wiki; IMDb)
Season 3: Dr. Angry Head (Christmas Specials Wiki; IMDb)
Season 4: The Ghost of Christmas Presents (Christmas Specials Wiki; IMDb)
Season 5: Chris-Mess (Christmas Specials Wiki; IMDb)
Ben 10
Season 3: Merry Christmas (Amazon; Christmas Specials Wiki; IMDb; Wikia)
The Big Bang Theory
Season 2: The Bath Item Gift Hypothesis (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; Wikia)
Season 3: The Maternal Congruence (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; Wikia)
Season 6: The Santa Simulation (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; Wikia; Wikipedia)
Season 7: The Cooper Extraction (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; Wikia)
Season 8: The Clean Room Infiltration (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; Wikia)
The Big O
Season 1: Daemonseed (IMDb; Wikia) Set on a Christmas-like holiday called Heaven's Day.
Black-ish
Season 1: Black Santa/White Christmas (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; Wikia)
Season 2: Stuff (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; Wikia)
Season 3: Just Christmas, Baby (Amazon; Christmas Specials Wiki; IMDb; Wikia)
Season 6: Father Christmas (Amazon; Christmas Specials Wiki; IMDb; Wikia)
Season 7: Compton Around the Christmas Tree (Amazon; Christmas Specials Wiki; IMDb; Wikia)
Bless the Harts
Season 1: Miracle On Culpepper Slims Boulevard (Amazon; Christmas Specials Wiki; IMDb; TV Tropes; Wikia)
Bob's Burgers
Season 3: God Rest Ye Merry Gentle-Mannequins (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; TV Tropes; Wikia; Wikipedia)
Season 4: Christmas in the Car (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; TV Tropes; Wikia; Wikipedia) This kind of reminded me of Jeepers Creepers.
Season 5: Father of the Bob (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; TV Tropes; Wikia; Wikipedia)
Season 6: Nice-Capades (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; TV Tropes; Wikia; Wikipedia)
Season 7: The Last Gingerbread House on the Left (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; TV Tropes; Wikia; Wikipedia)
Season 8: The Bleakening (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; TV Tropes; Wikia; Wikipedia) An hour-long musical.
Season 9: Better Off Sled (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; TV Tropes; Wikia)
Season 10: Have Yourself a Maily Linda Christmas (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; TV Tropes; Wikia)
Season 11: Yachty or Nice (Amazon; Christmas Specials Wiki; IMDb; TV Tropes; Wikia)
Season 12: Gene's Christmas Break (Amazon; Christmas Specials Wiki; IMDb; TV Tropes; Wikia)
Season 13: The Plight Before Christmas (Christmas Specials Wiki; IMDb; TV Tropes; Wikia; Wikipedia)
The Boondocks
Season 1: A Huey Freeman Christmas (Amazon; Christmas Specials Wiki; IMDb; TV Tropes; Wikia; Wikipedia)
Brooklyn Nine-Nine
Season 1: Christmas (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; TV Tropes; Wikia)
Season 2: The Pontiac Bandit Returns (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; TV Tropes; Wikia)
Season 3: Yippie Kayak (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; TV Tropes; Wikia)
Season 4: Captain Latvia (Amazon; A.V. Club; IMDb; TV Tropes; Wikia)
Buffy the Vampire Slayer
Season 3: Amends (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; TV Tropes; Wikia; Wikipedia)
Castle
Season 5: Secret Santa (Amazon; IMDb; Wikia)
Season 7: Bad Santa (Amazon; IMDb; TV Tropes; Wikia)
Chrono Crusade
Season 1: Holy Night (IMDb; Wikia)
The Cleveland Show (There were other Christmas eps, but these are the ones I remember.)
Season 2: Murray Christmas (Amazon; Christmas Specials Wiki; IMDb; Wikia)
Season 4: 'Tis the Cleveland to Be Sorry (Amazon; Christmas Specials Wiki; IMDb; Wikia)
Community
Season 1: Comparative Religion (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; TV Tropes; Wikia; Wikipedia)
Season 2: Abed's Uncontrollable Christmas (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; TV Tropes; Wikia; Wikipedia)
Season 3: Regional Holiday Music (Amazon; A.V. Club; Christmas Specials Wiki; IMDb; TV Tropes; Wikia; Wikipedia)
Season 4: Intro to Knots (Amazon; A.V. Club; IMDb; TV Tropes; Wikia; Wikipedia)
Dan Vs.
Season 2: The Mall Santa (Amazon; Christmas Specials Wiki; IMDb; Wikia)
Danny Phantom
Season 2: The Fright Before Christmas! (Amazon; Christmas Specials Wiki; IMDb; Wikia)
The Dead Zone
Season 4: A Very Dead Zone Christmas (Amazon; IMDb) Mainly what I remember about this is "The Most Wonderful Time of the Year" by Martina Sorbara.
Dexter's Laboratory
Season 2: Dexter vs. Santa's Claws (Christmas Specials Wiki; IMDb; Wikia) (One segment)
Dinosaurs
Season 2: Refrigerator Day (Amazon; Christmas Specials Wiki; IMDb; Muppet Wiki; TV Tropes) Set on a Christmas-like holiday (see episode title)
Dr. Quinn, Medicine Woman
Season 2: Dr. Mike's Dream: A Christmas Tale (IMDb; Wikia) There were other Christmas eps, but this is the only one I remember even vaguely.
Due South
Season 1: Gift of the Wheelman (Christmas Specials Wiki; IMDb; TV Tropes; Wikia)