Casey's "promise" of "16 different endings" ultimately proved untrue, but choices from previous games did effect the state of the galaxy at the end (or at least, was intended to). Sparing Wrex on Virmire, saving the Maelon's genophage research, and choosing whether or not to listen to the salarian Dalatross all effected the outcome of the events on Tuchanka (there is one outcome where, if Wrex is dead and Maelon's data was not saved, you can actually convince Mordin to not go up to the tower and instead join the Crucible project). Rewriting or destroying the geth Heretics and clearing the charges against Tali effect the outcome of the events on Rannoch. Saving Miranda's sister and giving her Alliance resources effects events on Sanctuary, saving the Rachni Queen and getting Grunt through his rite of passage effects events on Aralakh, helping Jack work through her issues effects events at Grissom Academy, etc., etc.
They don't all necessarily tie into the ending, and the fact that none of the specific "war assets" really tie into cinematics or gameplay in the final battle is a lamentable missed opportunity. But the circumstances of the galaxy are different in various ways by the end, depending on your choices, and this is reflected in the slides shown during the Extended Cut ending.
(of course, a lot of this is fundamentally undone by the mass relays being destroyed. Which is why I am glad they weren't destroyed in the Extended Cut).