Just occurred to me that there might not be one
Saiyan saga has kaioken which isn't technically a form but may as well be Frieza saga has super Saiyan, cell saga has super Saiyan grades and super Saiyan 2, buu has super Saiyan 3, bog has god, then blue, blue evolved and ui
Am I missing one?
Spoiler alerts, obviously:
None of DragonBall introduced new forms.
Beyond that it's a little more dicey on what you would call a new "form". A lot of archs had a power increase pre ssj1, but no form change. The radditz saga didn't have one. The vagita saga didn't have one, but the kio-ken burst move was implemented. The namek/Ginyu saga had no form changes but Goku became super strong while training under 100g gravity while going to Namek. The Dr.Gero saga had no new forms, but Vagita became a ssj1. Garlic Jr saga didn't have any but I wouldn't call that a major arch. It was more like filler. Ssj2 popped up at the start of the Bobbidy saga but flat lined there until the Buu saga. The otherworld tournament had no new ones.
That's all I can think of off the top of my head.
I think that depends on what you consider an arc. I would consider the entire time they're on namek the frieza saga