Why would dark matter collide with sodium iodide? In my readings of the DAMA/Libra dark matter detector articles, it is said to detect a dark matter particle by seeing light emissions from a sodium iodide crystal ion collision. My question is why would the collision happen if dark matter doesn't interact with ordinary matter?
 A: We know that dark matter does interact with ordinary matter through gravity. But gravity is very weak. So, indeed you are right: If dark matter /only/ interacts with ordinary matter through gravity, there is no reason to expect it to collide with the sodium iodine crystal.
Now, should we expect dark matter to interact with us in some other way? Interestingly, the average cosmological densities of dark matter ($\Omega_{darkmatter}$) and luminous matter ($\Omega_{baryons}$) are somewhat similar, $\Omega_{darkmatter}\sim 5\Omega_{baryons}$. That would be unexpected if gravity was the only connection between the two. Further, observations of scaling laws in galaxies also point towards a connection between the two that is much stronger than what one would expect from gravity alone. So, I think it is fair to say that yes, we should expect there to be interactions between dark matter and us other than just through gravity.
That still doesn't mean that dark matter, when it interacts with a sodium iodine crystal, would be visible in that experiment, given its detection principle, energy threshold,  etc. For that to be your expectation, you need to assume that dark matter is in the mass range typical of other particles and atoms (i.e. proton mass up to 1000s of proton masses), and that it has a sufficiently high scatter probability, like that from Z-mediation at loop level or through Higgs mediation. Dark matter particles that have these properties are called WIMPs; of course, many other dark matter models have been proposed.
