The only tattoos that are a no go are "prison tattoos" -- you know, anything on the extremities (hands, knuckles, feet and toes, tribal face tattoos, teardrop on the cheek, gang signs). Also, if you've got grills, I'd keep them at home too.
If you're concerned about post-MBA work -- keep in mind that the dress code at most places is business casual or suits -- where no one is going to see a dragon on your arms (or even forearms unless you want to wear short sleeved collared shirts which is even more of a fashion faux pas at work), or the Nativity scene on your entire back. Your clothing will cover all the most likely places you'll get a tattoo.
And if you are working at an office where you're allowed to wear shorts and t-shirts, then it's not the kind of place that will care what kinds of tattoos you have -- unless they are swastikas or gang acronyms.
And your MBA classmates for the most part won't really care unless you are inked in gang affiliations.
Hard to say how it works from one school to the next (or even one year to the next) -- but when I was in school, those who had tats and displayed them, wore earrings, were 420 friendly, dyed their hair pink, kept a Taliban beard, etc. did it as a badge of honor so to speak - it was a sign that "I'm not interested in traditional careers" or "I've already had a job lined up." Actually, the 420 friendly crowd when I was in school tended to be the Euros and west coasters anyhow who were going to jobs where there was no drug testing.