Wraith King is a hardy melee strength hero traditionally played as a carry in public matchmaking where he has a high win rate.
He is famed for only having one active ability – a damage-dealing stun - and three entirely passive abilities, the most notable of which is his ultimate, Reincarnation, which acts much like an Aegis of the Immortal and grants Wraith King a second life.
Skills
Wraithfire Blast is always skilled first and usually maxed first.
Vampiric Aura is usually skilled around level 4 or later, so that it doesn't push your creep wave out, and is maxed last.
Mortal Strike is usually skilled last but maxed second.
Reincarnation is always skilled (levels 6, 11 and 16). Make sure you always have enough mana for it to trigger - buy a Soul Ring if necessary.
Stats are taken early on once or twice, as they are more useful than your two passives early on.
Items
Starting Items: Tangos, Healing Salve, Quelling Blade (or Stout Shield), Iron Branches.
Early Game: Boots of Speed, Magic Wand, Hand of Midas (if good start).
Core Items: Phase Boots or Power Treads, Armlet of Mordiggian.
Luxury Extensions: Assault Cuirass, Black King Bar, Desolator, Heaven's Halberd, Abyssal Blade, Heart of Tarrasque, Mjollnir.
Situational Items: Soul Ring (burst mana for ultimate), Hand of Midas (good start), Divine Rapier (all-in late game), Drums of Endurance (early stats), Monkey King Bar (anti-evasion).