ANSWER
There was no film being shown aboard the Titanic when it hit the iceburg.
Many of you replied that the silent version of "The Posiedon Adventure" was being screened at the time. And I replied to many of you that you were correct. This based on an article from snopes.com, ordinarily a rock-solid reliable source of information. However, we all fell victim to what snopes.com calls "False Authority Syndrome". Had we looked a little closer, we would have seen that this particular article was in a section called "The Repository of Lost Legends", where they "don't let the truth get in the way of a good story". (And you have to admit, it was a good story.) Had we checked further, we would have seen that there are no other references to this story on the Internet, except for those referring back to the snopes.com article, and a few pointing out that it was a hoax. Had we checked the IMdb, we would have seen that the IMdb page linked to from snopes.com was a fake. Had we looked into the origin of The Poseidon Adventure, we would have discovered that the novel was first published in 1969. In short, we were had. And boy do we feel silly. (Well, at least I do.) Don't feel too bad though, they also fooled The Christian Science Monitor, The Naples Daily News, and countless message board posters all across the Internet.
The snopes.com disclaimer: http://www.snopes.com/lost/false.htm
WHO GOT IT RIGHT: Bob Milligan.