An answerer answers a question.
A defendant (or their lawyer) tries to defend themselves against a criminal charge in court.
A respondent (or their lawyer) responds to a motion in court.
As CopperKettle suggests, a replier replies to a statement or question.
A torture victim is someone who has been "put to the question" by the inquisition.
A witness is someone who testifies in court. They may be subject to examination and cross-examination by the lawyers, and answer the lawyers' questions.
An invitee RSVPs. (Répondez s'il vous plaît is French for "Respond if it pleases you.")
An interviewee answers a series of questions. Policemen ask questions of subjects, suspects, witnesses, and persons of interest. Employers interview job applicants. Journalists also conduct interviews. Talk show hosts interview guests and callers.