There are a few key technological advances that really define the stage of the game once research on them has been completed.
As mentioned in the previous section, the Class V Planetary Shields technology is one of those technologies. After this is researched, the usefulness of ships in protecting one's own colonies drops dramatically. After all, the planets will benefit doubly thus:
The best shield available for ships when Class V Planetary Shield becomes available is Class III Deflector Shield. This means the best ship shielding will reduce all hits by 3 damage whereas the planetary shield, when constructed will result in all missile bases reducing all damage by 8. Additionally, direct fire weapon damage is reduced by half against planets. That means laser type weapons will have their damage reduced by a whole 16 points when attacking missile bases after the lowest level planetary shield has been constructed.
This means that if you have ships in orbit, they will be attacked by all direct fire weapons and they will take quite a bit of damage in the process. If you don't have ships in orbit, the greatest portion of space used on the tech list of most enemy ships is completely worthless in combat.
Another literally huge technology that completely defines the rest of the game after it is researched is High Energy Focus, the level 34 Propulsion technology. This allows direct fire weaponry to literally reach halfway across the screen. An approxiimately equal level technology, the Auto Blaster, and an approximate 3 - 4 movement spaces per ship for that stage of the game in combat makes it so you can start tearing into their ships massively starting from the first or at the latest the second turn.
It is no joke that a lot of pro players equip this to every ship they ever make after it is researched, it is that powerful. Even better, most pro players build a new ship type to make maximum use of it the very same turn they research it and most of them probably begin production of that ship in huge numbers immediately.
As touched on earlier, the Death Spores weaponry, a level 11 Planetology tech is another very defining technology for it's stage of the game. Death ships, or ships equipped with large numbers of these weapons, are one of the most terrifying things in the entire game. These ships, when used by the enemies, pretty much force you to destroy them immediately or you lose your entire colony in a few short turns, no matter how big it is.
The combo pack of Atmospheric Terraforming, Soil Enrichment, and Advanced Soil Enrichment, is another set of game defining techs. The reason for this is because the AI does not commonly take the maximum advantage of them and this offers players the greatest opportunity to jump tremendously ahead of the opponents in terms of production. These technologies greatly increase the habitability and the maximum population of worlds they are used on and you generally want to use them on every applicable world as early as you can do so safely.
Note also, you NEVER want to trade any game defining tech to any computer controlled player. It almost doesn't matter what you get from them it is probably not worth it. The only time it really makes sense to trade any of these to the computer is if they will most likely steal it from you with spies anyway. If that is the case, get everything you can for it right away.
The Gauss Autocannon is another game defining tech when it is researched. It is the only weapon that both fires multiple times per turn AND halves the enemy's shield strength. Not only that, but it does damage to enemy ships even if they have the best possible shielding and it rips them to shreds if they don't have the best possible shielding. It is quite possibly the best weapon in the entire game. Even in the later stages it remains relevant against ships because of how many you can fit onto a ship in the later stages of the game. In other words, it is is driven purely by large amounts of brute force. When you are using this weapon, it is because you don't want to play around, you want to make ships flat out die.
The Gauss Autocannon also just so happens to be a level 32 Weapons Tech, almost exactly the same technological difficulty to research as the level 34 Propulstion tech High Energy Focus.
Note also that Advanced Soil Enrichment is a level 30 Planetology Tech and it is arguably better than Complete Terraforming, a 50th level Planetology Tech. Whether it is or not, the fact that it can even be argued shows just how good this tech is.
There are many techs that are really good, but these ones are probably the ones that are truly "game defining".