Draconomicon and Races of the Dragon listed numerous variants of Half-Dragon for non-Core Dragons.
(And magazines listed Half-Dragon variants for almost all Dragons in their articles)
Planar Dragons
Draconomicon:
Chaos Dragon is immune to compulsion; Half-Dragon - to Confusion (misheard?)
Radiant Dragon is immune to light effects; Half-Dragon gets nothing
Tarterian Dragon have no innate immunity (but three special qualities); Half-Dragon gets nothing
Dragon #321:
Arboreal Dragon is immune to Acid, Sonic, and Enchantment; Half-Dragon gets only resistance to Acid and Sonic 20
Beast Dragon is immune to Cold and Electricity; Half-Dragon gets only resistance to Cold and Electricity 20
Ferrous (Dr#356): Iron Dragon have Breath Weapon which deal half-Electricity/half-Fire damage; Half-Dragon's BW deal only Electricity damage
Steel Dragon is immune to Acid; Half-Dragon gets only +10 against Poison
Epic Dragons
Force Dragon is immune to Force; Half-Dragon gets nothing
Prismatic Dragon have Prismatic Spray as BW; Half-Dragon have Searing Light as BW