I've worked with a few athletes over the years that have vomited during workouts. Some were caused by late night partying the night before, but often they could be attributed to one or more of the following issues:
*The athlete being pushed too hard, too quickly - the athlete being inadequately conditioned for the given training session
Make no mistake about it - this is a failure on the coach's part and there is nothing good to be gained from pushing a client to the breaking point unless you want to somehow drive home the point that late-night partying or pre-season softness will not be tolerated. Even in those circumstances, I don't agree with or recommend it.
*Poor pre-training eating habits
I think the pre-training meal is largely an individual preference, and what constitutes "proper diet" can vary largely according to kind of training being undertaken, but there are certainly foods that "sit well" in the stomach, and foods that do not. If athletes are eating heavy foods in the hour immediately prior to intense workouts, that's trouble waiting to happen.
*Poor breathing patterns
Very intense training can cause a trainee's breathing to become spastic. Coupled with a dry mouth and throat, gagging isn't uncommon and if that persists, vomiting isn't far behind. Learning and drilling proper relaxation breathing patterns immediately following such exertions can go a long way toward avoiding "Pukey".