Strangely, while my favourite pairings are rarely the most popular ones in their fandoms, looking through my bookmarks I also have very few truly rare pairings there. It's not through lack of wanting them, though! Just hard to find long, good quality ones I suppose.

I do have 4 Giles/Cordelia (http://delicious.com/Lanta/giles%2Fcordelia) Buffy fics bookmarked. I have a strange love for that pairing. I think a couple of the fics are fairly long; the other two just ficlets.

I don't know enough about Alias fandom to know which pairings are most popular; how common is Sydney/Weiss? (When Stavros Met Sofia (http://chaos.horsechicks.com/stavrossofia.html), short but great fun.)

There's a Star Wars one that kind of fits... it's a rare pairing (Jaina/Wes) but the "pairing" is only there in terms of one character flirting with the other. Great fun although best appreciated by someone familiar with the EU and particularly Aaron Allston's "Enemy Lines" duo of novels. Those Rituals Pertaining to Courtship (http://www.fanfiction.net/s/2469608/1/Those_Rituals_Pertaining_To_Courtship).

Other than that, just some rare crossover pairings if those count:
An Equal Temper (http://carlyinrome.livejournal.com/336246.html) (Angel x Bones: Cordelia/Booth)
The Longest Three-Week Day (http://michelel72.livejournal.com/49511.html) (Doctor Who x Stargate Atlantis: Rodney/Donna)
Look But Don't (http://moodfic.livejournal.com/66649.html) (Buffy x X-Men: Rogue/Faith)