Regarding the Rabbit's Foot in MI3, there's no concrete explanation is what it was or what it could do, but this is what that IMF analyst says in the film:
"It's interesting - I used to have this professor at Oxford, okay? Doctor Wickham, his name was and he was, like, this massive fat guy, you know? Huge, big guy. We used to call him - you know, well, I won't tell you what we used to call him, but he taught biomolecular kinetics and cellular dynamics. And he used to sort of scare the underclassmen with this story about how the world would eventually be eviscerated by technology. You see, it was inevitable that a compound would be created which he referred to as the 'Anti-God'. It was like an accelerated mutator or sort of, you know, like a, an unstoppable force of destructive power, that would just lay waste to everything - to buildings and parks and streets and children and ice cream parlors, you know? So whenever I see, like, a rogue organization willing to spend this amount of money on a mystery tech, I always assume...it's the Anti-God. End-of-the-world kinda stuff, you know... [pauses, Ethan and Luther gaze at him thoughtfully] But no, I don't have any idea what it is. I was just speculating."
The device itself is also shown to have a "biohazard" symbol on it. So aside from its true purpose as the film's MacGuffin, I would wager the device itself was either some kind of extremely dangerous biological agent/substance/weapon or the key to developing such a substance/weapon.
It's true function obviously wasn't important and wouldn't have affected the story either way.
