Paul McGann played the Eighth Doctor. In terms of the Doctor's own timeline (as distinct from the running order of the show), that was the incarnation after the Seventh Doctor (Sylvester McCoy) & before the "War Doctor" (John Hurt). The Seventh Doctor regenerated into the Eighth in "Doctor Who", the TV movie. The Eighth Doctor regenerated into the "War Doctor" in "The Night of the Doctor".
The "War Doctor" regenerated into the Ninth Doctor (Christopher Eccleston) at the end of "The Day of the Doctor". That regeneration wasn't shown in full but "The Time of the Doctor" confirmed that there was no other incarnation of the Doctor between the "War Doctor" & the Ninth Doctor. Because the "War Doctor" refused to use the name "Doctor" (though others did use it of him), that incarnation isn't counted in the numbering.