I love it when people without any scientific background quote stuff that people with scientific backgrounds have told them, and get the whole thing wrong. S'kinda cute, like passive-aggressiveness or watching kids talking about who's Dad's the toughest =p
When ever someone tells you an object can't move faster than light, ask them "Relative to what?" Because, by basic relativity, if two objects have a speed limit of 0.9c (speed of light), and are moving in opposite directions to you, then they're both moving at their maximum speed in your frame of reference, however, in the reference frame of any of these objects, the other is moving at 1.8c, which is faster than a speed of light and oh dear I've gone cross-eyed... (of course that's ignoring the effects of travelling close to the speed of light with stuff like Lorentz Transformation and all that jazz I can't be bothered going into. There's an analytical solution that says relative to one object the other looks to be going at a completely different speed than it does to the observer between the two objects and whatnot. S'all very complex really, if you're interested in this stuff ask someone at your local university's physics department, you'll probably get thrown out by security, but hey, not harm in trying, right?)
Anyways, stand back, I have some science here! D=
It's a pointless question. You might as well ask what would happen if Buddha headbutted Satan.
Or, the comic book equivalent I know this is has probably been derived from, "What would happen if the Juggernaut ran into the Blob" (Answer: "To be continued in the next exciting issue!")
The moving object has to be moving relative to something. If you assume it's moving relative to the unstoppable object, then in the reference frame of this object, the unmoveable object is already moving towards them.
Though, as a physicist, making the assumption these objects can exist (as it's been stated a few times before, they can't), the most probable results would be that:
1. Both objects are annihilated.
2. Moving object passes through unmoving one.
3. Assuming the object is only unmovable in it's whole, the unmovable object would would break into it's separate components
4. Ditto for unstoppable object.
However, in a realistic scenario, an "unstoppable" object and an "unmovable" object are simple objects assumed to have an infinite mass, as their mass is much greater (ie, several orders of magnitude higher) than anything else. Ie, if you were comparing the collision of the earth and a tennis ball, it would be easier to model the earth as an unmovable object as it's mass is about 27 orders of magnitude higher than the tennis ball (a Tennis ball would have a mass of about 0.01 kg, while the Earth's mass is around 5,973,600,000,000,000,000,000,000 kg, 5.9736*10**24 kg, if you're smart). An unstoppable object in this case would be, say, Mars, if it had been displaced out of it's orbit and was heading directly towards your tennis ball. Mars has a mass of around 6.4185*10**23 kg, which means that when it hits earth it would slightly accelerate the Earth away from it. You'd also not be playing Tennis anytime soon, but that's a different story altogether!
I think it's funny how a lot of people love to blurt out this one rule of special relativity like they're some kind of mini-Einstein without actually having a full grasp on the most basic forms of relativity or mathematical modelling...