Well, the sun exploding would be impossible, as it would not go Supernova for another 5 billion years (As it is 5 Billion years old now). And... I doubt it would be a financial crash, because the Mayans had no idea of what future economy would be like..... Now, it could be that some force (maybe China) will declare war on the rest of Earth, or maybe the Mayans actually COULD predict that Earth would be pelted with Asteroids. I'm not sure. But, IMO, I wouldn't worry about it. It's like how in 2000 or 2002 whatever we though the world would end, but it didn't. I don't see the "end" coming. Using logic, it is quite impossible they could have predicted such a thing. The Mayans most likey thought something bad may happen on this day because of all the special circumstances that were happeneing (Leap Year, Winter Solstice, Sun crossing Galactic Equator or something)
Edit: Excuse me, Green Kirby's right, it won't go Supernova it will turn into a Red Giant