Updated: Because some characters have come and gone.
Bacardi and Cola -- Jack and Curtiss, when teamed on an op. Because Curtiss is dark skinned and Jack is light-skinned, and so they recall those respective beverages.
Badger --- Ivan Erwich, because the same actor, Mark Sheppard, played 'Badger' on Firefly. And he sort of looks like a badger. (Now deceased)
Biff Henderson --- Jack's Nemesis Christopher Henderson, named for David Letterman's stage manager. I arbitrarily decided this was funnier than calling him RoboCop.
Cartman's Mom --- Lynn McGill's crackwhore sister, after the character of Cartman's Mom on South Park who is also a crackwhore. (Now deceased)
Chiggy Killer - Bill Buchanan. So-called because in his previous role on Space: Above and Beyond, actor James Morrison's character of Lt. Col. TC McQueen took out the infamous alien ace, Chiggy von-Richthofen. Or, I should say, shot down. "Took out" could be mistaken as some weird, alien, Brokeback Mountain dating experience.
Cougar Bait --- Kim Bauer, because of the notorious Season 3 incident in which she was menaced by a cougar.
Comrade HATO --- Vladimir Bierko. HATO means "Hallowed Are the Ori," since the same actor played a Prior (Priest) in the Cult of the Ori on Stargate SG-1.
Dick Cheney --- Mike Novick, because he sort of looks like vice president Dick Cheney.
Florence Henderson --- Biff Henderson's wife, after the mom on the Brady Bunch... who was probably a bigger skank than she let on, but that's speculation for another time.
Hannibal Connery -- A terrorist collaborator who died in the Feburary 6, 2006 episode, but looked and sounded like a cross between Hannibal Lecter and Sean Connery.(Now deceased)
John McCain --- Cartman's Mom's boyfriend. Because he appeared on the show the same week Senator John McCain was rumored to be making a cameo appearance. (Now deceased)
Potato-Face --- Television Without Pity's nickname for Chloe, because of that scrunched-up face she always makes and because it's a much less cruel nickname than Rene Zellweger-face.
President Weasel --- President Logan because... c'mon.
Mary Todd Weasel --- Martha Logan, because she shares the bipolar disorder associated with another first lady, Mary-Todd Lincoln.
Murphy --- President Weasel's VP, after SeaLab 2021's Commander Murphy, because he proposed imposing 'Martian Law' on Los Angeles.
S4GF -- Audrey Raines. Stands for Season 4 Girl Friend, because she was Jack's girlfirend in season 4 until he got her husband killed. Hey, I've done worse things in relationships. There was an S5GF with a teenaged son affectionately named Hairboy, but I don't think we'll be seeing them again.
Sam Gamgee -- Lynn McGill, because Sean Astin played Sam Gamgee in the Lord of the Rings Trilogy.
Sid Blumenthal --- Sleazy, conniving presidential aide Walt Cummings, so named because he recalls a sleazy, conniving presidential aide from the Clinton Admin named Sid Blumenthal.(Now deceased)
Studboy --- Spenser, because he serviced Chloe in a stud-like manner, although it looks like he's gone for the rest of the season.
President Subaru --- The Russian President, because the character's name kinda sorta sounds like "Subaru," which is a kind of Japanese car favored by liberals who can't afford Volvos.
Red Foreman --- Secret Service agent Aaron Pierce, who sort of looks vaguely like That 70's Show's Red Foreman, but mostly because it enables me to use the word "dumbass" a lot.
Redshirts --- The CTU Security Personnel, because they were red shirts and are every bit as expendable as Star Trek Security Personnel, who also wore red shirts.
Token --- Curtiss's nickname when not teamed with Jack, after the character of 'Token Black' on South Park, because with David Palmer dead, Curtiss is the only African-American left in the regular cast. (I bet he has a bass guitar in his basement, too.)
Tom Green --- Cougar Bait's new boyfriend, because he has a goatee and he's really annoying.
Truffle Shuffle - Edgar, because he's a big guy and his gait recalls the shildhood-obesity dance performed by the character of Chunk in the movie The Goonies, which I have never actually seen, but am told it suits Edgar.(Now deceased)
Zombie Edgar --- Holding this in reserve... just in case.