The One Ring was forged in Mount Doom in J.R.R. Tolkien's legendarium.
Mount Doom is the volcano in Mordor where Sauron makes the One Ring. Its Elvish name is Orodruin, meaning “Mountain of Blazing Fire,” so Mount Doom and Orodruin are two names for the same place rather than separate answers.
The Ring can be destroyed only in the fire where it was made. This makes Mount Doom the destination of Frodo Baggins and Samwise Gamgee during their attempt to end Sauron's power. The mountain's fires also represent the industrial and destructive force associated with Mordor.
A common mix-up is to treat Orodruin as a different volcano. It is the Sindarin name used for Mount Doom. Mount Gundabad and Mindolluin are other mountains in Tolkien's world, but neither forged the One Ring.