This question was asked in the JRR Tolkien birthday thread and someone suggested that it be made a separate thread of its own, so voila!
What would have happened had Beren not recovered the silmaril from Morgoth’s crown? Say Elwë hadn’t objected to Beren’s intention to marry Luthien. Or say Beren simply failed in the quest.
My take on it is that it would leave Thingol alive and ruling the Sindar through the time of the LOTR (as opposed to his murder by the Dwarves for the Nauglamir with the silmaril on it).
This would be a moot point, however, since it would also leave Morgoth to rule Beleriand and Middle-Earth for the lifetime of Arda. Without the silmaril in the possession of Thingol’s heirs, there is no successful attempt by Ëarendil to pierce the enchantments isolating Valinor from the rest of Arda, and so there is no Great Host to come and remove Morgoth from the world and defeat his armies.
The sons and nephews of Fëanor are picked off one by one as Morgoth’s armies creep across the lands around Beleriand. Eventually, even Beleriand itself will fall, since Melian’s enchantment has the strength of a single maia, no matter how wise in magic she might be, while Morgoth has his own Vala-level strength as well as multiple maiar on his side (including Sauron).
I see a refugee scenario, the Sindar and the remainder of the surviving Noldor fleeing into Eriador and, eventually, over the Hithaeglir, creating separate nations in the forests of which Mirkwood/Greenwood was a remnant, and perhaps preventing the rest of that primeval forest from being destroyed with their greater might and power than the sylvans had.
But the eleventh-hour rescue by the hosts of the Valar, the Teleri and the Vanyar, never happened because there was no silmaril.