Doc Martens were heavy lace-up boots or shoes with air-cushioned soles.
The Ninth Doctor wore black Doc Marten boots. (TV: Rose, etc.) right up to his fall after the Battle of the Game Station against a fleet of Mark VIII Daleks of human origin led by their Emperor and his Elite Guard. (TV: The Parting of the Ways) His successor, the Tenth Doctor, wore them in his first hours. (TV: The Parting of the Ways, Born Again, The Christmas Invasion)
Ace was fond of wearing Doc Martens boots, (COMIC: Fellow Travellers, The Good Soldier, PROSE: Timewyrm: Apocalypse, Cat's Cradle: Warhead, Heritage, The Time and Tide) and said that London was the best place to buy them. (PROSE: Untitled)
Bernice Summerfield wore Doc Marten boots during her wedding to Jason Kane. (PROSE: Happy Endings)
The Fugitive Doctor wore black Doc Marten boots. (TV: Fugitive of the Judoon, The Timeless Children, Once, Upon Time, The Power of the Doctor)
Behind the scenes
The brand was misspelled "Doc Martin" in The Time and Tide.