This might not be very related, since the thread is called
Tolkien's Deus ex Machina, and I'm going to speak about the movies. They, for one, are deus ex machinism at its highest height. (To overestimate a bit...
)
Movie deus ex machinas
1) The earthquake and crack caused by the fall of Barad-Dûr
Just consider the scene of the battle of Morannon. Somehow the land cracks just between the heroes and the baddies, even circling the heroes who are surrounded by enemies, to safety. In my opinion that is one of the most ridiculous scenes in the whole movies. I understand it must have been difficult to show the sudden fall of Sauron's army, but that wasn't a very good way of doing it.
2) Elves in Helm's Deep
And that was a totally unnecessary one!
I admit it can be debated whether it's a deus ex machina at all, since the Elves don't provide a very easy victory, just victory.
3) Arwen
Arwen who saves Aragorn from drowning. Admitted, this is not a proper deus ex machina, because Arwen is not there to save Aragorn from drowning, but Aragorn is drowning for Arwen to save him.
Actually it seems I came up with one real movie deus ex machinba and two movie false deus ex machinas...
Anyway, I'll leave them be there on the list. I'm sure there is more, but my brain doesn't work well enough to bring them up atm.