The Goblin is the Japanese name for what FF1 through FF4 called the "Imp" in English translations. Characteristically, the weak Goblin looks like a little elf/gnome with pointy ears and a dagger. The Imp is stronger, purple-skinned, flying, and can cast strong magic. FF7 was the first to start using "goblin" properly. To further confuse you, Imp was also a status ailment in FF6 (see Species for more info). In FF4, Goblin was summonable by picking up the "Goblin" item it leaves behind sometimes. Its "Goblin Punch" is a mainstay in Blue Magic.
NOTE: The "Goblin" enemy in FF6 has no relation whatsoever to either the imp or goblin.
-Black Goblin (Dawn of Souls)
-Knocker (Dawn of Souls)
-Imp (NA) / Goblin (JP)
-Grey Imp (NA) / Goblin Guard (JP)
-Imp (NA) / Goblin (JP) (SUMMON)
-Dark Imp (NA) / Killer Goblin (JP)
-Imp Captain (NA) / Goblin Captain
-Tricker (NA) / Lil' Murder (JP)
-Gobbldigoo (NA) / Gobbledegook (JP)
-Goblin (many varieties)
Although there are no goblins in the game, the Baknamy enemies use their classic Goblin Punch.
ATK: Goblin Punch
Brownie (NA) / Goblin (JP)
-Mint Mint (NA) / Knocker (JP)
-Gobbledeguck (NA) / Gobbledegook (JP)
Similar to FF12, the Baknamys take over the mantle of the Goblin enemies.