The War of the Jewels:

This war lasted almost from the rising of the Sun until the end of the First Age of the Sun. It was between Morgoth and the Eldar, after the Dark Lord stole the Silmarils. Unfortunately it eventually ended up with elf fighting elf, due to the the Oath of Fëanor:
Then Fëanor swore a terrible oath. His seven sons leapt straightaway to his side and took the selfsame vow together, and red as blood shone their drawn swords in the glare of the torches. They swore an oath which none shall break, and none should take, by even the name of Ilúvatar, calling the Everlasting Dark upon them if they kept it not; and Manwë they named in witness, and Varda, and the hallowed mountain of Taniquetil, vowing to pursue with vengeance and hatred to the ends of the World Vala, Demon, Elf or Man as yet unborn, or any creature, great or small, good or evil, that time should bring forth unto the end of days, whoso should hold or take or keep a Silmaril from their possession. Thus spoke Maedhros and Maglor and Celegorm, Curufin and Caranthir, Amrod and Amras, princes of the Noldor; and many quailed to hear the dread words. For so sworn, good or evil, an oath may not be broken, and it shall pursue oathkeeper and oathbreaker to the world's end. (S.97-98)

The war was never fully successful, probably due to the doom placed on the Noldor for their deeds in leaving Valinor.
Tears unnumbered ye shall shed; and the Valar will fence Valinor against you, and shut you out, so that not even the echo of your lamentation shall pass over the moutains. On the House of Fëanor the wrath of the Valar lieth from the West unto the uttermost East, and upon all that will follow them it shall be laid also. Their Oath shall drive them, and yet betray them, and ever snatch away the very treasures that they have sworn to pursue. To evil end shall all things turn that they begin well; and by treason of kin unto kin and the fear of treason, shall this come to pass. The Disposessed shall they be forever. Ye have spilled the blood of your kindred unrighteously and have stained the land of Aman. For blood ye shall render blood, and beyond Aman ye shall dwell in Death's shadow. For though Eru appointed to you to die not in Eä, and no sickness may assail you, yet slain ye may be, and slain ye shall be: by weapon and by torment and grief; and your houseless spirits shall come then to Mandos. There long shall ye abide and yearn for your bodies, and find little pity though all whom ye have slain should entreat for you. And those that endure in Middle-earth and come not to Mandos shall grow weary of the world as with a great burden, and shall wane, and become as shadows of regret before the younger race that cometh after. The Valar have spoken. (S.103-104)

By the end of the War of the Jewels, one of the Silmarils was in the sky with Eärendil, as the Evening Star, another had been thrown in the ocean, and the third into a crevasse in the earth.

War of the Dwarves and the Orcs:

War between the Orcs of the Misty Mountains and the Dwarves, lasting between the years 2793 and 2799 of the Third Age. It ended with the Battle of Azanulbizar, in which the Dwarves were victorious. The Orc population had been reduced enough to make passage through the mountains safe for the next century or so.

The War of the Ring:

The events of the years 3018 and 3019 of the Third Age. For more information, see the calendar on this site.

The Watchful Peace:

The years between 2063 and 2460 of the Third Age. Sauron remained hidden in Dol Guldur and the Nazgûl were quiet within Minas Morgul.

The Lord of the Rings
The Silmarillion
The Unfinished Tales
The Hobbit
The Complete Guide to Middle Earth by Robert Foster