What are the names of all the Doctor Who companions?

In order: Susan Foreman, Ian Chesterton, Barbara Wright, Vicki, Stephen Taylor, Dorothea "Dodo" Chaplet, Ben Jackson, Polly, Jamie Macrimmon, Victoria Waterfield, Zoe Herriot, Elizabeth Shaw, Josephine "Jo" Grant, Sarah Jane Smith, Dr. Harry Sullivan, Leela, K-9, The Lady Romanadvoratrelundar ("Romana"), Adric, Nyssa, Tegan Jovanka, Turlough, Perpegillium "Peri" Brown, Melanie Bush, Dorothy "Ace", Rose Tyler, Dr. Martha Jones, Donna Noble, Amy Pond.

One-off companions who didn't last more than one show include Katarina, Sara Kingdom, Dr. Grace Holloway, Astrid Peth, and Lady Christina de Souza. The companion Kamelion appears in two shows, not successively.

There are also recurring characters who are not quite companions, such as Brigadier Lethbridge Stewart and the UNIT members with Doctor 3 and 4 particularly. The new series has a number of non-companion or quasi-companion recurring characters, of whom Capt. Jack Harkness comes closest to being a companion.