What other kinds of games are like Hero Quest...? In that, what other games are around with a degree of character development (although not the depth of something like D&D), items etc, that actually takes place on a board...?
I'm not chasing something like Munchkin Quest, as your character does not carry over from session to session.
I think of the greatest of this kind is Descent: Journeys in the Dark especially with Road to Legend expansion which makes carrying over your characters between sessions slightly easier.
There has been a D&D board game.
Descent is definitely the good current choice, especially with either of it's campaign expansions. (You don't need both campaigns; they largely overlap so one is enough, unles you play it roughly every night for a year.) Although, get one of the standard expansions Well of Darkness or Altar of Despair first; the campaign plays much better with the treachery cards from those expansions.
For a simpler, faster (and harder!) option, Descent's 'kid brother' Doom can work well.
(While we're on the family, Descent's older uncle Runebound is a bit less Hero-Questy but may still match what you're looking for.)
Descent is a great game, but it's designed to play every level almost from scratch, unlike Hero Quest. While the Road to Legend expansion allows for a campaign, its game play suffers a lot and gets very boring soon.
Unlike Descent, in Doom you keep your character as the game progresses. It has similar, simpler, rules. If you don't mind dying over and over ^^
A very similar is World in Shades
