I seriously considered using that one half-dragon beholder picture here, but decided to go with some wholesome HotDQ villainy instead.
Half-dragon boosts strength, intelligence, dexterity and charisma, as well as natural armor. The first is especially increased, which I'm sure melee characters will be overjoyed to hear.
There is (of course) also a type change to dragon, which is neat because it qualifies one for a plethora of goodies. Being a half-dragon further enhances some of those, such as Dragonfire Inspiration.
Creatures with RHD can also enjoy more skill points and HP, as a neat added bonus.
Finally, there's the natural weapons and breath weapon. The former consists of two near-worthless claws (I like wielding weapons), and a bite (sure, more attacks are nice). The latter is a 1/day (boooo) ability to deal 6d8 damage.
Just from this, one might think a +1 LA is barely justifiable. I disagree there: half-dragons have a lot of side material and variant abilities that warrant a +2.