The Lord of the Rings showed all the main races of Middle-earth, but Men, Elves and Hobbits were the primary players. Meanwhile, the Dwarves (besides Gimli) only played limited roles. They got their moment in the spotlight in The Hobbit, where Thorin Oakenshield led Bilbo and a company of Dwarves to reclaim the Lonely Mountain from the Dragon Smaug. The thing is, Smaug wasn't the first Dragon to kill and terrorize a Dwarvish stronghold. In fact, there was a long history of conflict between the two races.
The War of the Dwarves and Dragons started in T.A. 2570 lasted about 20 years. It started because Sauron gave seven rings of power to the seven Dwarf Lords, which gave them Dragon Sickness. So, they created the legendary Seven Hoards, and that attracted the attention of the greedy, gold-loving Dragons that lived in the Grey Mountains. The war ended when the Dwarves abandoned the Grey Mountains. However, in all the documented conflicts with Dragons, it was never a Dwarf that dealt the killing blow.
Bard the Bowman Killed Smaug in The Hobbit
Smaug was LOTR's best-known Dragon. He was the main antagonist in The Hobbit, and his lair was the abandoned Dwarf kingdom of Erebor. In the book, Thorin wanted Smaug dead for revenge, but Gandalf also wanted him dead -- to prevent an alliance between Smaug and Sauron. However, it wasn't Thorin or Gandalf that vanquished Smaug. It was a man named Bard. He was a resident of nearby Lake-town and the descendant of the Lords of Dale. When Bilbo made Smaug mad, the Dragon went and attacked Lake-town. So, Bard defended his people by firing a black arrow into a weak spot on Smaug's underside, which killed him.
Túrin Turambar Killed Glaurung, The Father of Dragons
The Lord of the Rings' first Dragon was created by Morgoth, who couldn't make life on his own accord. So, when he created the first Dragon, he must have perverted something good and made it into his evil servant. That first Dragon was named Glaurung, and the fire-breathing drake helped win a number of battles. However, Glaurung was eventually killed by Túrin Turambar, the most tragic warrior of the First Age. He killed Glaurung with his sword, but shortly after, he killed himself with the same, cursed sword.
Eärendil Killed Ancalagon the Black
Middle-earth's largest Dragon was Ancalagon the Black. He was a spawn of Glaurung, but he was fully grown by the end of the First Age and ready to fight in the War of Wrath. Ancalagon's exact size wasn't known, but when he fell from the heavens, he destroyed all three peaks of Thangorodrim. The one to cast him down was none other than Eärendil the Mariner. When things were dire for the Noldor, Eärendil (who was a half-Elf and Elrond's father) was the one that went to Valinor and sought the aid of the Valar. When he returned, Eärendil came in force and fought the Dragons until he smote Ancalagon.
Fram of the Éothéod Killed Scatha
While there were plenty of other Dragons in LOTR, Scatha was the last one to receive a name. Unfortunately, Scatha's name was the only thing that Tolkien explained about the Dragon's early life. Yet, he did detail Scatha's demise. Somehow, Fram of the Éothéod killed the great beast. However, it was what happened after Scatha's demise that was most interesting. Fram had killed the beast, so he laid claim to the hoard. Naturally, the Dwarves didn't like that, and Fram's only response was to send them a necklace made of Dragon's teeth. For the insult, the Dwarves found Fram and killed him, though they never reclaimed their hoard.