What are different Types of Transformers

    1 Power transformers

•      Laminated core
•      Toroidal
•      Autotransformer
•      Variable autotransformer
•      Induction regulator
•      Polyphase transformer
•      Grounding transformer
•      Leakage (or stray field) transformers
•      Resonant transformer
•      Constant voltage transformer
•       Ferrite core
•       Planar transformer
•       Oil cooled transformer
•       Cast resin transformer
•       Isolating transformer

    2 Instrument transformer

•         Current transformer
•         Potential transformer (Voltage transformer)
•         Combined instrument transformer

    3 Pulse transformer
    4 RF transformer
        4.1 Air-core transformer
        4.2 Ferrite-core transformer
        4.3 Transmission-line transformer
        4.4 Balun
    5 Audio transformer
        5.1 Loudspeaker transformer
        5.2 Output transformer
        5.3 Small signal transformer
        5.4 Interstage and coupling transformers
    6 Other types
        6.1 Hedgehog
        6.2 Variometer and variocoupler
        6.3 Rotary transformer
  

Source Wikipedia