Having covered masturbation let’s take this on, staying away from the obvious ones like “technicolor yawn” etc.
My absolute favorite of all time is “Calling Ralph and Huey on the big porcelain phone.”
Chunder.
Hurl.
Ruth.
Along those lines, I once heard a woman refer to it as ‘praying to the porcelain god’. Whenever she needed to take a break she’d say that she felt ‘another prayer session coming on’.
Another one I liked was ‘letting up the cargo’.
Go see Uncle Ralph/Earl
Lorch
Upchuck
Blow groceries
HEAVE!
One summer, my parents, aunt, siblings, and I took a car trip from Ohio to Florida and back. Grandma (aunt’s and dad’s mother) suggested we take along a container similar to this one, just in case any “accidents” should occur. The traveling party held a jocular debate concerning whether the official name of the receptacle should be the “puke pail”, the “upchuck urn”, or the “vomit vase” (with vase pronounced as VAHZ, since that’s the “hoity-toity” way to say the word).
Hork.
Hurl.
Blow chunks.
I think, next time I need something like that, I’m going to call it the “upchuck urn”.
Yack.
Shout at your shoes
Technicolor yawn
Launch lunch
Though I doubt it’s in popular use now, during the age of sail, an “Admiral of the Narrow Seas” was someone who puked on the lap of the person infront of him/her.
Driving the porcelain bus.
HEY! I was supposed to say that!!!
I’ll be the third to mention “technicolor yawn”. 
My most common expressions are “throw up” and “ralph”, but I did find myself using the expression “chunder” last week, which was rather unusual. Must be the Brit influence in my history. I also use the expression “toss one’s cookies”.
Spew.
Sick up.
Lose your cookies?
Not me. I’m classier than that. I’m gonna call it the “vomit vahze.” 
My family spent a lot of time on boats. We called it “looking for Ralph,” because you’d lean over the side of the boat and call out “Ralph! Ralph! Ralph!”
And on an international note: I understand that in the land down under, women blow and men chunder.
Nothing better than this as yet.
I can’t believe I’m the first one to say barf, im guessing because its so common. I love it though, its a classic. “My dog barfed all over my shoes”
Two buddies were talking in a bar.
“Man, I got so drunk last night, I blew chunks!”
“It’s cool, dude, happens to the best of us.”
“Naw, bro, you don’t understand! Chunks is my dog!”
emesis
“Selling Buicks”
“Getting another look at your lunch” (and it doesn’t improve on second viewing)