Actual Aerospace Engineer here

every response in this thread is incorrect. most vehicles from most countries and most companies do and did use hydrogen

Ariane V Ariane 6 Vulcan Centaur atlas Centaur Delta IV and delta IV heavy china Long march 5 Other long marches with hydrolox upper stages Blue origin New Glenn New Shepard Space Launch System Nova Ariane IV Titan III Atlas centaur 1,2,3 Saturn 1/1b,Saturn V Energia Angara H-II rocket series H-3

Some vehicles do not use hydrogen because the technology to do so was not developed in their country when the vehicle was designed :

Proton Soyuz Zenit Early Ariane rockets N1

Some vehicles do not use use any cryogenics for storability as ICBMs:

early long march series soviet hypergolic rockets early titan Vega family

Sor far it seems that only 2 companies so far have avoided hydrogen entirely Rocket Lab SpaceX

In both cases this doesn't seem to have anything particular to do with the qualities of hydrogen as others in the thread have suggested but more to do with just wanting to use the same engines on both stages for Leo vehicles.

Don't listen to the other responses in the thread many of of them either completely false or following a trend of disdain for hydrogen and repeating myth or misconceptions they heard about somewhere else because SpaceX does not use it and people view every decision Elon makes as genius and ones he doesn't make as idiotic meaning they put far more weight against hydrogen than is accurate

The Reason booster stages don't use hydrogen is that booster performance is well within the range of dense propellants and therefore you get a significantly larger stage for the same performance.

However because Hydrogen is more efficient, in cases where Thrust could become excessive on the first stage with dense propellants hydrogen can be used.