Luckily, most (but not all) of the times I've heard it were in jest. Today, randomly, I decided to see if there was any truth to the claim, and the answer is interesting. As it turns out, the details are still debated amongst scholars, who generally agree that he was kinda-sorta against meat eating... sometimes. But historical accuracy is irrelevant to the story, so I'll go ahead and present the side that's interesting.
"Do you know that your Führer is a vegetarian, and that he does not eat meat because of his general attitude toward life and his love for the world of animals? Do you know that your Führer is an exemplary friend of animals, and even as a chancellor, he is not separated from the animals he has kept for years?...The Führer is an ardent opponent of any torture of animals, in particular vivisection, and has declared to terminate those conditions...thus fulfilling his role as the savior of animals, from continuous and nameless torments and pain." —Neugeist/Die Weisse Fahne (German magazine of the New Thought movement)(Emphasis mine). Here's an (nth-hand) description from Wikipedia regarding the BBC series "The Nazis: a Warning from History":
In this series an eyewitness account tells of Hitler watching movies (which he did very often). If ever a scene showed (even fictional) cruelty to or death of an animal, Hitler would cover his eyes and look away until someone alerted him the scene was over.Why is this interesting? Well, these and other anecdotes actually do suggest that, regardless of his dietary habits, Hitler was actually able to empathize with animals. In fact, upon further reading, it seems unequivocally established that he was quite fond of dogs -- as were at least some of his compatriots.
So the warning that Hitler was a vegetarian seems to be saying something after all. It's a solemn reminder that the ability to empathize is not enough. That "being good" in some particular regard is no guarantee that our moral compass is set straight. But maybe it's also a source for hope: that even in the most seemingly lost causes, that twinkle of humanity deep down is never fully extinguished.
Lest I lose more of my audience to boredom, rest assured I'll have more science and less pontificating in the near future :)