Apart from the Kinslayings at the hands of the Sons of Fëanor, the worst of evil deeds that weren't of Melkor's doing was The Ruin of Doriath. As told in the 22nd chapter of the Silmarillion, even after the Battle of Unnumbered Tears, in which the last hope of Elves and Men rallying against Melkor was destroyed by the treachery of the Easterlings, The Realm of Doriath still survived under protection of Melian the Maia. (One could wonder why Melkor didn't rally Sauron and the Balrogs, and attempt to overcome her power.)
During the time, Húrin, a man of heroism, but his spirit broken by Melkor, had been released from Melkor's fortress of Angband and wandered across Beleriand. During Hurin's wanderings, he came to the ruins of Nargothrond, where he came into possession of the Nauglamir, the Necklace of the Dwarves. Hurin took the Nauglamir and made his way to Doriath, where the Elves took him from the borders to King Thingol's halls in Menegroth. In Menegroth, Hurin gave the Nauglamir to Thingol as a gift, and it is said that Hurin then went and cast himself into the western seas.
With him Thingol still had the Silmaril that Beren and Luthien took from Melkor's crown. The Silmaril filled his thought, and he decided to have it bound into the Nauglamir. For this, the King summoned the Dwarves of Nogrod, who worked in the forges of Menegroth as Thingol looked on, awaiting his treasure to be made. As they presented the work to Thingol, the lust and charm of the Silmaril overcame the Dwarves, and they decided they should take the Silmaril for themselves, under the excuse that the Nauglamir was not made for Thingol. Thingol saw through this and attempted to gain it back through right argument. With Thingol's defense, the dwarves turned to rage, suddenly they grabbed him and slew him as he stood. Thingol fell to the ground in death, "...And with his last sight he gazed upon the Silmaril."
After the Death of Thingol, Melian left Beleriand, seeing no further purpose there, and the protection she gave Doriath was also gone. So, returning to Nogrod, the dwarves lied to their kin about what happened in Doriath (though lust for the Silmaril certainly clouded their reasoning) and a great force of Dwarves came from Nogrod and sacked Menegroth, and the rest of Doriath.
Mablung, a valiant soldier of Doriath, sent a messenger with the Silmaril to Beren and Luthien in Ossiriand before he died defending Menegroth, because of this act, Beren was able to ambush the Dwarves on the return to Nogrod as they crossed the Gelion with a force of Green Elves, but Doriath was lost. Beren took the Nauglamir with the Silmaril, and his wife, Thingol's daughter, Luthien, wore it, and eventually it made its way back to Valinor, but that is another tale.
So, one of the last remaining Havens of the Elves was lost, not to the orcs of Melkor, but to the treachery of the Dwarves through lust for the Silmaril of Feanor. If we give any thought to it, we can see that the Silmarils, though they preserve the light of the Trees of Valinor, tend to only bring sadness in Middle Earth. The Jewels of Fëanor were truly not meant for Elves or Men, but for the whole of Arda to preserve the lost Bliss of Valinor.