The shortest Doctor is the Seventh, played by Sylvester McCoy, at 168cm.
Matt Smith's Doctor, the Eleventh, was 180cm tall.
The title of Tallest Doctor is shared by the Third (Jon Pertwee) and Fourth (Tom Baker) - each 191cm tall.
Full List: Three (191), Four (191), Ten (185), Five (184), Six (183), Nine (183), Eleven (180), Two (175), One (174), Eight (174), Seven (168). The War Doctor and the Twelfth Doctor are not included in this list. All numbers in brackets are the Doctor's height in centimetres.