All characters:
To get back to default stance (standing, facing opponent): hold H
While sidestepping: u,u or d,d
While running: from 1 or more body lengths away, f,f(hold)
Akira:
(no special prerequisites)
Alpha-152:
Juggling opponent: ub+P
(That should've been called "While floating" instead of "Juggling opponent")
Ayane:
With back to foe: u+P
Bass:
With back to foe: f+P+K
Bayman:
With back to foe: d,db,b+P
Brad Wong:
With back to foe: b,b+P
Lying with legs facing foe: d+P+K
While lying: same as "Lying with legs facing foe" (or do "Lying with head facing foe" and f/b reverse the command)
During Dokuritsu-Ho: b+K
Lying with head facing foe: df+P+K
During handstand: f,f+P+K
During reverse handstand: b,b+P then f,f+P+K
Christie:
With back to foe: b+P
During Jakeiho: u+P+K or d+P+K
Eliot:
With back to foe: b+P
Gen Fu:
With back to foe: b,b+P (miss with this move, or opponent will end up in front)
Hayabusa:
With back to foe: df+P+K
During Ongyoin: d+P+K
Hayate:
With back to foe: u+P
Helena:
With back to foe: b+P
During Bokuho: d+P+K
Hitomi:
With back to foe: b+H+K
Jann Lee:
With back to foe: b,b+P
During Dragon Stance: f+P,b
Kasumi:
With back to foe: b+K
During Hoshinpo: df+P+K
Kokoro:
With back to foe: db+K
Leifang:
With back to foe: b+P
During Unshu: b+P+K
Lisa:
With back to foe: u+P
Mila:
(no special prerequisites)
Pai:
With back to foe: b,b+P
During Bokutai: b+K,d
During Meishouho: b+P+K
During Hakkeshou: f+P+K,uf+P+K
Rig:
With back to foe: b,b+K
During Bending Stance: b+P+K
In Turn Leg Cut: f+P+K
Sarah:
With back to foe: b,b+P
In Flamingo Stance: b+K
While stepping: b+K then db+P+K
While stepping forward: f,f+P+K
Tina:
With back to foe: b,b+P
Zack:
With back to foe: b,b+K
While Ducking: d+P+K
While Swaying: b+P