He was first partnered with a young boy named Wallace, or Willis in the English version, and was the twin of the digimon Lopmon who was actually based on a rabbit.
In the original japanese version, Terriermon is named "Gumimon", after his babyII/in training stage. Lopmon is named after his babyII/in training stage in both versions, and is referred to as Cocomon.
The second and most recent time Terriermon was included in Digimon was in Season 3, Digimon Tamers, partnered with Henry Wong (a different Terriermon, however).
This Terriermon is where we have the phrase "momentai" from (also written as moumentai) which translates as "take it easy" or "relax", which sums up the tiny digimon nicely, calm and layed back, a reluctant fighter.
His most notable move is his "petit twister" or "Terrier Tornado" in the dub, in which he spins his long ears quickly to create a mini twister with great force.
"Growlmon! Where could he be hiding? This should be like trying to find a haystack in a haystack!"