1. S1E6: Katara going to prison to break out Haru and ends up liberating the entire prison from the fire nation (you could say technically it’s one of those ‘everyone else escaped’ situations, but I think it counts)
2. S1E13: Zuko breaking Aang out of Zhao’s prison as the Blue Spirit
3. S2E18: Sokka and Toph breaking the Earth King out of imprisonment
4. S3E7: Toph and Katara breaking out of prison with Katara’s waterbending
5. S3E8: Hama breaking out of prison using bloodbending
6. S3E11: Iroh breaking out of prison on the eclipse
7. S3E14/15: Breaking Hakoda, Zuko, Suki, and Chit Sang out of the Boiling Rock
8. S3E19: Bumi breaking out of his imprisonment on the eclipse (flashback)
Kidnapping/Hostage/Ransom/Semi-Imprisonment Situation Escapes
1. S1E2: Katara and Sokka rescuing Aang from Zuko’s ship
2. S1E9: Katara being held hostage by pirates and escaping
3. S1E15: Katara and Sokka being taken hostage by Zuko and June
4. S2E1: Zuko and Iroh escaping just before they were official prisoners of Azula
5. S2E3: Bumi technically breaking free from his metal prison, only to voluntarily return to it
6. S2E6: Toph breaking Aang out of his hostage situation from the Earth Rumble lineup
7. S2E7: Zuko freeing Lee from his capture by the soldiers
8. S2E17: Zuko freeing Appa from the lake laogai prison
9. S2E18: Sokka and Toph saving the Earth King’s bear from Mai and Ty Lee
10. S3E8: Toph freeing Hama’s prisoners out from under the mountain
+ honorable mention: S2E5: Aang goes to prison for a murder Kiyoshi committed 300 years prior and does community service for it