The chocobo riding glitch in the SNES and PS versions of Final Fantasy VI happens when a guest character is the party leader and the player tries to ride a chocobo. The only instance in which this glitch can occur normally is during Banon-Edgar-Terra's scenario, after they reach the end of the Lethe River and arrive on the overworld map. There is a hidden chocobo stable in the forest on the edge of the desert just southwest of Figaro Castle. If the player rides a chocobo with Banon as the party leader, his sprite will appear to be glitchy, with the lower portion of his walking sprite animation pasted on the chocobo's back and his head being cut off. This glitch was fixed in the GBA version, in which Banon's riding sprite is replaced with Terra's. This glitch was also fixed in the Pixel Remaster, where Banon was given new sprites.
The glitch occurs as a result of most guest characters lacking chocobo-riding sprites and as a result using random unrelated data as their graphics instead. Presumably they were not given any as, aside from Banon, none of them can encounter a chocobo stable. Banon lacking graphics was most likely an oversight due to there being only one stable he can reach that is secret and easy to miss.
This glitch can also occur with Leo, the two Ghosts, Kefka, a Terra who is permanently in her esper form, Locke in Merchant clothes, and Celes in her opera clothes. Banon is the only character who can experience this glitch in normal gameplay, however, Merchant Locke's glitched graphics can be seen without hacking by exploiting the bypass event glitch, while Leo's and the Ghosts' can be seen by exploiting the Airship glitch. Cheats or hacks are required to see the others' glitched graphics as, even with glitches, there is no known way to have them in the party at a point that the glitch can be triggered.
There is a bugfix patch that the player can use to fix this glitch in the SNES version. Unlike the GBA version, this fix adds a new riding sprite for Banon.