The battles of the Noldor and their allies the Sindar, the Dwarves, and the men of Beleriand against Morgoth in the First Age of Sun. Also called the War of the Jewels, since they were fought to recover the stolen Silmarils. There were five great battles and numberless smaller engagements.
The First Battle of Beleriand, otherwise nameless. King Thingol and allies versus Morgoth's orcish armies. Winner: Thingol and Co
The Dagor-nuin-Giliath, the Battle under Stars, so called because it was fought before the first rising of the Sun. A rough equivalent of the Normandy landings, fought by Feanor and his followers. A crushing victory for the Noldor.
The Dagor Aglareb, the Glorious Battle. The greatest (and last) victory of the Noldor over Morgoth.
The Dagor Bragollach, the Battle of Sudden Flame. The tide of the war turns. Morgoth's dragons and Balrogs prove unstoppable. From here on, the forces of good would be steadily pushed back and their citadels destroyed one by one.
The Nirnaeth Arnoediad, the Battle of Unnumbered Tears. The lowest point of the war. The last efforts of the Noldor and their allies are crushed. Afterwards, most of the leaders of the Elves, Dwarves, and Men are dead, in hiding, or prisoners of Morgoth. Things are so bad that Earendil finally sails west to seek aid from the Valar.
The Great Battle and the War of Wrath. The Valar and their armies utterly crush Morgoth's power, scatter his armies to the four winds, and imprison him until the end of time. The two remaining Silmarils are given to Feanor's sons Maedhros and Maglor.
Other noteworthy battles: the Sack of Nargothrond and the Fall of Gondolin.