Lets Start With THOTD original...
Thomas Rogan: Player 1 in House of the Dead and briefly player 1 in THOTD3. He also appears in THOTD2 as a cameo in the Good Ending.
G: The series' most reoccuring character and playable in every single game except THOTD4.
Sophie Richards: Rogan's fiance, a scientist for the DBR corporation and the subject of the endings for the first game (good ending, sophie is alive and well, bad ending, sophie is a zombie and normal ending, no one knows what happened to her...)
The Magician: The most reoccuring boss in the series appearing 3 times in THOTDs 1, 2 and 4SP. When he was made, he decided not to listen to Curien's commands and merely decides to kill everybody and everything. This changes in THOTD2 as he obeys Goldman (strangely) and he also agrees to protect The Emperor during incubation.
James Taylor: He is player 1 in THOTDs 2 and 4 and in both of the games, he has a score to settle with Goldman. Sadly, in THOTD4's final cutscene, during the battle with Goldman's resurrected form, The World, he sacrifices himself to kill Goldman's final creation and true masterpiece.
Harry Harris: He and Amy Crystal were in charge of evacuating the civilians of Venice because they might get killed otherwise. Sadly, Harry was badly injured at the hands of a giant zombie called The Strength while James and Gary where at the underground passage battling The Tower...