"F*@%ing asshole Mable" or words to that effect are fairly frequent too.
And someone singing "Ooh Glooooooooomweaver, I believe you can get me through the na-haight," or "It's the Final Wasteland! De de de duh, de du de duh duh..."
<Edited for language - Rabit>
If I could give you a thumbs-up here, I would.
We always have an idiot yelling "FINISH HIM!!" when he brings the villain down to 1 or 2 HP, pretty much handing him over to the next player...
That idiot is usually me...
other Mortal Kombat yells include "Come here!/Get over here!!" when grappling hook is played... "Toasty!!" for any number of Ra's moves... and "Fatality" when a hero kills another hero just for fun when we know we have the game in the bag.
"Ping" when doing exactly 1 damage with someone, Chrono-Ranger does a lot of pinging at the beginning of the game.
"Flip out" when someone uses an effect to play a card from the top of the deck e.g. Omnitron-X or The Scholar.
And I say "Wooo!" when someone lets me draw a card out of turn (or when I play a card that does).
I've also gotten a lot of players to chant "Flip, flip, Flipadelphia!" from Always Sunny in Philadelphia when a villain character card flips (and some of them haven't even seen that episode!).
We have a few...
Plink- general exclamation meaning that damage didn't get through due to damage reduction
Zorch- anytime Young Legacy's base power is used.
Thwack- any sort of melee hit
"Stealth bot!" Said anytime the person running the villain can just stop talking beacause stealthy is just taking all the damage and nullifying.
"Human Shield" has become a popular "stealth bot!" alternative at my gaming table.
Any time a hero target causes itself psychic damage, we refer to it as "emotional damage."
Ooh, someone's mention of Savage Mana reminded me that I also tend to refer to Haka as "eating" cards when he puts them beneath it, and usually accompany this with an "om nom nom" :D.
I also do the "Doo-doo doo doo, doo-doo doo-doo-doo" thing when speaking of the Final Wasteland.
Oh, and I see I'm not the only one to say "It's a trap!" when fighting against Ambuscade :D.
On the DnD-related things, I also think of the Adept as a Bard, though if I'm referring to him by anything other than his title, it's usually "Mr Drake".
I refer to damage reduction as "soak" (from my EQ days).
I sometimes refer to multiple-target damage as AE, but sometimes call it multi-hit.
We do the Final Wasteland, and Gloomweaver.
Raptor Bot I always throw down a Grimlock impression, "Raptor Bot no like Omnoitron!"
As Visionary when I use Precognition I alway say "and that's half the battle," a somewhat convoluted GI Joe reference.
Close Quarters Combat will often get a "now it's time to fight with Knives!" often followed by the Knifing around song. (Space Ghost reference)
Tempest gets tons of Lost Skeleton "On Marva we call lightning. . . " jokes.
The above has led to emphatic cries of "You can't make aliens dance" when Adept tries to buff Tempest.
The Tumbleweed from Time Cataclysm gets the "OH NO, THE TUMBLEWEED!" panic and freaking out. We frequently then prioritize destroying it with environment destruction effects, I still don't think we've ever attacked it, but it did get End of Days played on it, and once chastised.
"You suck Legacy" is a common theme in our games, with Iron Legacy or the Hero version, usually after he draws a card we don't need him to have, or IL pounds us, It has been directed at Champion Bot a few times as well.
I have a firend who can't help but sing "who'll stop the rain" whenever Tempest heals.
We definitely do refer to the card from Dawn's deck as "That Card," it shall not be named.
"For America!" gets called a lot with Legacy playing.
Stealth Bot is "Bot, Stealth Bot." when played.
Oh, and for some reason Throat Jab tends to get a "Crotch Shot" when it's played.
Lots of singing and wierd refrences in our group, the above are the decent and reasonably humorous results, it gets much worse.
"I also wonder…"
Seriously, that is SUCH a good movie! I'll have to remember that one next time I'm playing Tempest!
All of Tempest's attacks deal fish damage.
Legacy "raises the flag" when he uses Galvanize. If he has Inspiring Presence, he's raising two flags.
"Legacy charges! Motivationally!"
You also say, "Everyone draw a card!" in a very particular way with the same inflection each time which is difficult to describe here. It's like you're using the words "everyone draw a card" but you're really saying "Wooo!" 
The only Sentinel Slang I've had when playing with the Girlfriend and her 11 yearold has been for Akash'bhuta.
Whom we refer to as OshKosh B'gosh.
Apostate - A prostate We really didn't enjoy our first games against him.
Argent Adept - Hargent Hadept (some accent thing from someplace we picked up)
Expatriette - Hexpatriette
Chrono-Ranger - Go go Chrono Ranger!
I"ll update as I think of more.
Omnitron-X - Omnitronks (thanks to the GTG forums for starting that one...only I also call Omnitron Omnitronks)
Whenever Omnitron-X plays reset, we say "Boop!"
Wagner Mars Base - Vagner Mars Base (German accent)
Whenever Aurora plays, we say "Aurora Revolution!" Usually followed by "I'm a lemming!" From Battle Arena Toshendin. One character, a girl with a whip, had a move where she would spin around and say "Aurora Revolution!" and half the time the move would cause her to fall off the battlefield, to her death.
We also do the Final Countdown for the Final Wasteland.
When Legacy uses Motivational Charge - "For Great Justice!"
Whenever a boss's damage gets redirected to themselves: "Quit hitting yourself! Quit hitting yourself!"
Whenever Omnitron-X is going to take care of something: "Beep boop. I got this."
Rocket Punch - "Rocketu Puncho!"
Lightspeed Barrage - "Kachu Tenshin Amaguriken!" (Chestnuts roasting on an open fire technique from Ranma 1/2
Ground Pound - "Haka smash!"
Unity - "Unity!" - The Dave Shappel Show
Wraith uses Stealth or Stealth Bot blocks damage - "Nin nin nin!" (Flonne from Disgaea)
The Dude - The Scholar
Ooh, you just reminded me of another couple I use...
I sometimes say "Ctrl-Alt-Delete" when playing Reset on Omni-10.
I also say "Vahgner" for Wagner, but...that's because that's how it's pronounced, or so I assume.
I don't think I've yet exlcaimed "For Science!" when playing Tachyon or Unity (or Omni-10)...but I probably should at some point ;).
Alfred Bitchcock...that's rich!
I generally don't call the characters by their proper names. They all have shifting words that I throw around when they hit the table.
We've Huggy (Haka), Rat (Wraith), Ex-Patty/Ex-Paddy Wagon (Expatriette), Legs (Legacy(ies)), Abs (Absolute Zero), OmniX (Omnitron-X), Citizen Dune (Dawn), Bunkie, Mr Fixit, Tacks, etc.
Bunker has a Potato Cannon, everything he does is referred to as BUDDABUDDABUDDA!!
Kismet has a song sung titled 'It'll Be Okay' about implied incest. No reason, other than kismet being a lyrci in it.O
Oh, golly! This list would be endless if I actually sat here and thought about it. I use code words for everything, in every game ever.
Here's one I just remembered from one of my groups.
Polyphoric Flare (Argent Adept) becomes "Polyphonic Spree."
We use a lot of these, too. But a few seem unique to our group.
"Flick" is one damage that actually gets through. Comes from Magic the Gathering.
"Tanky McTankerton" -- the Scholar -- particularly with Flesh to Iron.
"Absorb" -- whenever damage reduction is sufficient to make damage become zero. Or "sucks it up".
Lots of acronyms -- "BB, AGL, TLT, AA, AZ, ..."
Ess-pite instead of Spite (so it's two syllables)
"Tank Card" -- any damage reduction card played by a hero
Cherry-man instead of Chairman
We tend to say "Burn it with fire!" a lot when Ra is in play.
Fanatic is hard to describe -- the first syllable is like a sports fan. "FAN -a-tick".
Whenever we can choose damage type, it's always "banana damage".
Arathorn
P.S. I'm sure there are more, but those are all that came to mind.