Initial plans were to give curly hair to the Second Doctor, to play up his quirkier personality as compared to his predecessor, though when the team saw him in the wig everyone hated it (Patrick Troughton said he looked like Harpo Marx and would often joke that Tom Baker stole his look). Anneke Wills (who played the companion Polly) combed Troughton's hair into the iconic messy moptop as a last-minute replacement.
Speaking of Tom Baker, the Fourth Doctor had some majorly curly hair. The curls were Tom Baker's natural hair, and meshed well with Four's characterization as goofy, cheeky, and anti-authoritarian to a greater extent than any incarnation before or since. Tellingly, when Four's personality became more melancholy and wizened in his final season, his curls turned into a softer '80s perm, the result of Baker's hair straightening out from burnout after seven years in the role.
Paul McGann, who played the very Cloudcuckoolanderish Eighth Doctor, got some bright ideas about buzzing his near-shoulder-length curls off between the audition and filming. So they made him wear a wig (which gets obviously frizzier throughout the Made-for-TV Movie). He once stated in an interview that hair generally seems to be an important part of playing the Doctor. His eventual insistance that the Eighth Doctor didn't still have the curls, in a Big Finish photoshoot where he kept his buzzcut, conveniently coincided with the Eight Doctor audios getting Darker and Edgier.