For me, a lot depends on sugar content. For some reason, alcohol+sugar=headache. So no dessert wines, no schnapps, no sweet mixed drinks for me. Just one is enough to make me go for the acetaminophen and water.
If you're talkin' with my preferred drinks, I'd say something along the lines of 12 shots of 100 proof whiskey is enough to make me regret drinking quite so heavily. Still, I can come down from that with water and time and not feel worse for wear. I don't puke off just whiskey, just (good) beer, or whiskey then beer short of full-on alcohol poisoning (which I've done before. That was about half a fifth of Gentleman Jack and 66 ounces of Arrogant Bastard. Worst birthday idea ever).
As for what it takes to make me puke... mixing it up between various liquors and beers. about 6 random drinks, all different, will have my stomach roiling badly. If I keep drinking and don't run for the water, I'll empty my stomach after that.
I'll just throw my hangover qualifications in here, too. Drunk+water+sleep=no hangover. Drunk+water-sleep=zombie me, but no hangover. Drunk-water=hangover, regardless of sleep. All a hangover is is a dehydrated body trying to flush alcohol.