This is obviously not a complete or definitive list -- comment below with your suggestions for what I should have included!
Low - "Long Way Around the Sea" (1999)
The slowcore pioneers Low issued the album Christmas in 1999 with little fanfare; the collection has since become a minor classic. Eschewing irony, it's a gentle celebration of the Christmas story -- the band members are Mormons, after all -- and "Long Way Around the Sea", about King Herod, Jesus and the wise men, is a powerful piece of music that sounds simultaneously ancient and thrillingly new.
Camera Obscura - "The Blizzard" (2009)
"Listen to that northern sigh. If we don't get home we'll die." So sings Tracyanne Campbell's rider to her lame pony, Dan, in this cover of the Jim Reeves standard. Like many songs of winter, the theme here is homecoming -- a lover waits seven miles away for the travellers to return as a snow blizzard descends, with the wind howling "mighty like a woman's screams". Contrasted with the unfeeling coldness of nature are "hot biscuits in the pan" (for the rider) and "hay so soft and warm" (for Dan). When Bing Crosby sang, "I'll be home for Christmas, if only in my dreams," the pathos was derived from knowing that, in reality, he probably wouldn't be. Reeves's lyric takes this further and (spoiler alert) has both rider and pony die, just a hundred yards from their destination. Glasgow's Camera Obscura began as a Belle and Sebastian-endorsed tweecore band; over ten years, they have grown in stature and ambition with each record. "The Blizzard" is a cover version but it's a good showcase for their classic pop sensibility, which delivers all the more impact for its restraint.
Trembling Bells and Bonnie "Prince" Billy - "New Year's Eve Is the Loneliest Night of the Year" (2010)
Will Oldham (aka Bonnie "Prince" Billy) has long cultivated the persona of the scatological romantic: his grimy narratives are often violent and sexually explicit but always full of passion and real emotion. In this respect, he resembles both Charles Bukowski and Shane MacGowan -- and he seems to channel the spirit of the Pogues singer here. "New Year's Eve . . ." is a seasonal song of the old school, complete with horns, strings, a big chorus ("It had to be in winter!") and vocal harmonies. Most of all, it evokes the Pogues hit "Fairytale of New York" and matches its sense of unbridled celebration.
Flaming Lips - "Christmas at the Zoo" (1995)
By the mid-1990s, the Flaming Lips were on their seventh album (Clouds Taste Metallic) and going from strength to strength, their preoccupations with aliens, the universe and animals still fresh and free from any hint of self-parody. A decade later, they would release Christmas on Mars -- a bizarre sci-fi movie that was one part Tarkovsky to two parts Ed Wood. "Christmas at the Zoo" was a taste of what was to come. Like Jeffrey Goines in Terry Gilliam's film Twelve Monkeys from the same year, the protagonist of the song decides to "free the animals all locked up in the zoo". The snakes, seals, llamas, birds and kangaroos, however, refuse to accept his help: "All of the animals agreed they're not happy at the zoo/But they preferred to save themselves." Wayne Coyne's lazy, drawling vocals are, as ever, a joy and the arrangement is perfectly off-kilter.
Quasi - "Merry X-mas" (2006)
Quasi's Sam Coomes and Janet Weiss are better known as members of Heatmiser and Sleater Kinney, respectively; both were members of Elliott Smith's touring band and they have served individually as members of Stephen Malkmus and the Jicks, Bright Eyes, Wild Flag and Jandek's live band. Perhaps because of this, Quasi has unfairly been regarded as a kind of side project, even though their seven official albums (mostly released by Domino) are among the best alternative pop records of the past two decades. They are also one of the most visceral live acts around - this despite Coomes's sugar-coated melodies that recall Brian Wilson, Paul McCartney and the Flaming Lips in equal measure. "Merry X-mas" is a barbed, five-minute exercise in self-loathing disguised as a piece of festive fun. "I was a crab, dragging claws through the mire/Down below in the murky depths of nowhere," Coomes sings. And that's just in the first two lines.
Emmy the Great and Tim Wheeler - "Home for the Holidays" (2011)
Of the year's indie Christmas songs, this collaboration between Emmy the Great and Tim Wheeler stands out in large part for its unashamed sentimentality. It's like a John Hughes movie in song form and the video (imagine EastEnders, as scripted by Nick Hornby) adopts seasonal clichés with good humour. "Did you ever write that book? Did you ever make it out of here?" sings Emmy -- questions that most of us do our best to avoid.
Gorky's Zygotic Mynci - "Christmas Eve" (1999)
Gorky's was always a modest group -- a delicate Welsh band that folded just as the nu-folk movement they helped to inspire was entering the indie mainstream -- and this brief twinkle of a song captures them at their most understated. Where other Christmas songs (not least several of the above) tend towards Spectorised bombast and kitsch, "Christmas Eve" only announces its subject in its final moments, after an extended, vaguely Spanish-sounding instrumental: "The star you fell in love to comes out on Christmas Eve."
Grandaddy - "Alan Parsons in a Winter Wonderland" (2000)
Last year, Jason Lytle, formerly of Grandaddy, gave away a set of piano instrumentals on his website as a Christmas present to his fans. The collection's simplicity was in keeping with the aesthetic of Lytle's first solo album, Yours Truly the Commuter (2009), which stepped back from the spaced-out eccentricities of his band's output while retaining the imaginative flourishes we have come to expect. Such flourishes are amply on display on "Alan Parsons in a Winter Wonderland", which reworks the old Christmas chestnut as a tribute to the prog-rock producer and engineer Parsons (best known for his work with Pink Floyd and his own group the Alan Parsons Project). What could have been an industry in-joke is redeemed by its deep affection for its subject, which permeates both the warm, synth-based production and the lyrics: "In the meadow, we could build a snowman/And pretend that he is Alan Parsons . . ."
Dump - "Another Lonely Christmas" (2001)
It's easy to forget that, as well and R'n'B and hip hop, Prince has cast a long shadow over alternative rock -- compare Ryan Adams's "Hotel Chelsea Nights", say, with "Purple Rain". James McNew, bassist for Yo la Tengo, surprised fans and critics alike with his 2001 album That Skinny Motherfucker with the High Voice, issued under his Dump moniker. Skinny consists entirely of songs by Prince, reinterpreted as lo-fi, post-rock doodles, and McNew's versions bring to the surface the exhilarating melancholy of the originals (an aspect of Prince's writing that is all too often overlooked). This is no truer than on "Another Lonely Christmas", a movie in miniature about love, death and loneliness. I couldn't find a YouTube video online, but it can be streamed here.
Bright Eyes - "Blue Christmas" (2002)
Like Low, Bright Eyes released a whole album of Christmas songs in collaboration with his Saddle Creek label mates and their cover of "Blue Christmas" was its highlight. The lead singer, Conor Oberst, opts for an impassioned but straight-ahead performance that manages to capture the spirit of the season without resorting to sleigh bells or any other Christmas gimmick.
That's my list, off the top of my head. So -- any other suggestions?
Finally, I couldn't resist doing a new one of my own. I've done a few before, including "Yo Zushi's Christmas Story", which appeared on the 2005 album Songs from a Dazzling Drift, and the 2009 song "Another Song di Natale" (both on Pointy Records); in a (festive) spirit of competition, here's "Merry Christmas", which you can download for free on Soundcloud.
Yo Zushi works for the New Statesman. His music is released by Pointy Records.