Characters you would have loved to have seen as a companion?

Ara (The Underwater Menace)
Preston (Warriors of the Deep)
Norna (Frontios)
Hugo Lang (The Twin Dilemma)
Katz (Timelash)
Vena (Timelash)
Natasha and Grigory (Revelation of the Daleks)
Ikona (Time and the Rani)
Ray (Delta and the Bannermen)
Alison Williams (Remembrance of the Daleks)
Professor Rachel Jensen (Remembrance of the Daleks)
Susan Q (The Happiness Patrol)
Earl Sigma (The Happiness Patrol)
Richard Maynard (Silver Nemesis)
Mags (The Greatest Show in the Galaxy)

Duggan (City of Death)
Seth (Horns of Nimon)
Todd (Kinda)
Mace (The Visitation)
Griffin (Attack of the Cybermen)
Herbert (Timelash)
Natasha (Revelation of the Daleks)

Will Chandler.

Lamia (Androids of Tara)
Rodan (Invasion of Time)
Mace (The Visitation)
Glitz (Mysterious Planet, Dragonfire)

Ancelyn (Battlefield)
Orcini (Revelation of the Daleks)
Mags (Greatest Show in the Galaxy)
Nancy (The Empty Child/The Doctor Dances)
Pex (Paradise Towers)
Mace (The Visitation)

These are from the top of my head atm.

Janet the flight stewardess in Vervoids. Yolande Palfry

Rodan (played by Hilary Ryan)  in Invasion of Time. That said Mary Tam arrived in the subsequent story and i wouldnt want to lose her.

Maybe Jessica Martin who played Mags in The Greatest Show in the Galaxy. But find a reason to change her name. The name "Mags" just grates.

Pamela Salem who played Rachel Jensen in Remembrance.

Richard Willis who played Varsh (Adric's brother) in Full Circle.  When Adric patronisingly said "I got a badge for mathematical excellence" to poor old Keera, Varsh could have turned round and punched him to the ground and then beaten him to a pulp. The Doctor could then have stepped forward and said "I understand what you did there Varsh and i understand why. Come, join me in the Tardis and we can explore the Universe together with Romana. Don't bother burying him". Cue grams.

Will and Jane from Awakening.