Searching for "Top 10" lists in the Internet gets you over 700 million returns. Seems people like them, so here's my first foray into the genre.
By pivotal, I mean an event that rendered a far different Texas than would have existed had it not occurred.
This is just my list. I'm not claiming it's definitive. Your list might look totally different.
10 - Invention of Barbed Wire - open range cattle raising was great for the herd owner, but hard on his neighbors. Economists call that a negative externality. The enclosure of the range was the first step in turning cattle raising into a modern industry.
9 - Advent of the Colt Revolver - can't underestimate what a difference-maker this weapon was in the Texas Rangers' campaigns against the hostile tribes.
8 - Annexation - had annexation not occurred, Texas would likely have hitched herself to Great Britain in some way out of financial need.
7 - Stephen F. Austin's Leadership - Anglo settlement of Mexican Texas would have occurred without Austin. But without his skill at tempering the passions of colonists, Anglo Texans might well have worn out their welcome before strong communities had time to form.
6 - Battle of the Alamo - some say the sacrifice of the Alamo garrison bought time for Sam Houston and the army. Others disagree. I'm including it here because it was pivotal in shaping the Texan psyche.
5 - Centralists Take Control of Mexico - had the Federal Constitution of 1824 remained in effect, and given Austin's continuous encouragement of the colonists to be good Mexican citizens, it's possible Texas would have become Mexico's Quebec.
4 - Deep Water Ports - it's commerce that leads to prosperity, and that means stuff must be moved from place to place. The creation a Texas' deep water ports at the turn of the twentieth century had a tremendous impact on the growth and economic welfare of Texas.
3 - Spindletop - January 10, 1901, the day the Lucas Gusher came in, should be proclaimed the official start of the twentieth century. Texaco, Gulf and Exxon can all trace their roots to that hill near Beaumont.
2 - Willis Carrier Invents the Air Conditioner - before air conditioning was common in Texas, members of the British Diplomatic Corps serving here were entitled to hazard pay because of the heat. Just like their comrades serving in Nigeria and Kenya. Without air conditioning, it's doubtful three of the ten largest cities in the US would be in Texas.
1 - The Battle of San Jacinto - The keystone in the arch of Manifest Destiny. Without this victory there would have been no republic...no state...no Texans.