There are many ways for a hero to die...
Heroic Sacrifice - Varian Wrynn, Broxigar etc. They give their life protecting their companion, buying time for them to escape/delay the Legion.
Treachery - Highlord Morgraine, Saurfang Jr etc. Backstabbing family/allies are the only way to bring these tough guys down.
In Vain - Vol'jin. watched brave heroes die in vain. Vol'jin's death pissed a lot of people off because it feels a character's potential wasted, but sadly, that's the truth for a lot of heroes, be it history or fantasy.
Corrupted - Arthas, Garrosh etc. The character didn't actually die, but the "Hero" inside them is no more. Character death usually follows.
Old Age - Lei Shen (Supposedly, but Chronicle told us the real story). The Hero is so tough that only time can bring them down.
I didn't put a vote up simply because there are just way too many other ways for a hero to die.
My personal favourite is Old Age, where a Hero died after surviving impossible amounts of odds and saving the world countless time. Near the end, the hero lies in his/her deathbed, surrounded by loving family and friends/worshipers, knowing that the he can trust the world to them and dies peacefully.
It's just ironic that Blizzard's hero never die from Old Age despite it's my favourite Hero's Death.
What is your favourite "Hero's Death"?