I'd have to say all of the recent teen-pop "original" Christmas songs belong on that list. Hilary Duff, NSync, Backstreet Boys, etc.
But there's a special place on that list for Jessica Simpson's whole Christmas album, "Rejoyce". Yeah, I get the "joy" thing, but the spelling of that word put me in a not-so-kind frame of mind before I even heard one note of the thing. And then, she tried to do "O Holy Night", which, just NO. As mentioned above, you need range to sing that song and she just can't do it. I hated my younger cousins for submitting me to that.
One of my favorite Christmas(ish?) songs is "Heat Miser/Snow Miser". Both the original and the Big Bad Voodoo Daddy version of it. I could listen to that song over and over and over - any time of the year.
Also, Matthew Ryan's take on "Little Drummer Boy" is a gem.
And I'll throw my hand up in support of "Do They Know It's Christmas". My take on the song has always been that those words are spoken to "us", in a slightly snide way ("well, tonight thank God it's them, instead of you") and not so much about bringing them Christmas as to tell us to wake up and share what good fortune we have.
Of course, I'm a child of the 80's. This song combined the massive power of fully operational LeBons, Stings and Bonos, so yeah, it's partially nostalgia. (Although, I have a tendency to believe it led to Sting lending vocals to Arcadia's "The Promise", which would automatically give it a free pass for just about anything, in my book).
Off to put on "Heat Miser", dammit.