The Doctor and Susan's escape from Gallifrey

For many pressing reasons, (TV: Twice Upon a Time) the First Doctor and his granddaughter stole a TARDIS (TV: The War Games) and fled their home planet. (TV: An Unearthly Child)

Build up
Either because he was bored, (TV: The War Games) scared, (TV: Heaven Sent) curious, (COMIC: Return of the Daleks) or through a combination of the above, (TV: Twice Upon a Time) the First Doctor felt he and his granddaughter, Susan needed to leave Gallifrey, (TV: The War Games) though he did intend to return, one day. (TV: An Unearthly Child)

Escape
to be added

Aftermath
After having many travels (TV: An Unearthly Child-The War Games) the second incarnation of the Doctor was caught by the Time Lords, and prosecuted for stealing the TARDIS and flouting the non-interference policy. (TV: The War Games)

After being recruited by the Celestial Intervention Agency, (PROSE: World Game) the Doctor escaped the Time Lords under a self-imposed exile. (COMIC: Action in Exile)

The Time Lords eventually found him, and imposed a forced regeneration on him, finally carrying out his sentence. (COMIC: The Night Walkers)

In later incarnations, the Fifth and Twelfth Doctors would also go on the from the Time Lords and Gallifrey. (TV: The Five Doctors, Hell Bent)