Two main types, which become moveable shapes for going up the neck -
Ddim7: xx0101 - also = Fdmi7, Abdim7, Bdmi7
Bbdim7: x12020 - also = C#dim7, Edim7, Gdim7
The third is really the Ddim7 shape moved up one fret
Adim7: x01212 - also = Cdim7, Ebdim7, F#dim7
So between these three open position dim7 shapes you can cover all 12 possible dim7 chords!
What are your favourite open-position dim7 chords?