In 1836, Colonels Crockett, Travis, and Bowie, along with 188 Texan soldiers fortified the Alamo, an old Spanish mission in preparation for an attack from several thousand Mexican troops led by General Santa Anna.
After a 13 day siege, Santa Anna attacked the mission on 6 March. Despite a heroic effort by Travis and his troops, Santa Anna would ultimately be victorious in eliminating all of the Texan rebels in what history would later remember as the Battle of the Alamo.
In 2374, a holosuite program recreating the battle was designed by Miles O'Brien and Julian Bashir aboard Deep Space 9. (DS9: "Wrongs Darker Than Death or Night") O'Brien was to play the role of Crockett; Bashir the role of Travis. Because Garak, who was contracted for making their clothes, was busy decoding messages for Starfleet Intelligence, Bashir offered the role of Crockett to Garak as incentive to hurry up on their costumes. O'Brien was not amused with the offer. (DS9: "Afterimage")
After experiencing the battle, they later had a heated discussion on the subject in Quark's. O'Brien believed that Santa Anna executed Crockett at the battle, supporting his position with the fact that Santa Anna didn't care about the "rules of war," and therefore would have considered the execution a point of pride.
Bashir, however, felt that Crockett was quite old for his time, and that his best days were behind him and that he was surviving on nothing but reputation. He believed that due to these factors, he would not be a man who would fight to his last breath in a clearly hopeless battle. He believed Crockett ultimately surrendered, to which O'Brien neither agreed nor disagreed with, noting that either way, there was no proof.
Worf, however believed that they were both wrong and that the only question is whether of not they believe in the legend of Crockett. If they did believe, then there would be no doubt in their minds that Crockett died the death of a hero. If they did not believe, then Crockett was just a man, and it did not matter how he died. (DS9: "Once More Unto the Breach")