Alliance
Baron Ashbury, Lord Walden and Lord Godfrey, once loyal followers of the Gilnean king Genn Greymane, betrayed the Gilnean defenders once it was revealed that the king had been affected by the worgen curse. Baron Ashbury and Lord Walden were slain in the resulting battle, while Lord Godfrey committed suicide. All three were raised into undeath and served the Forsaken for a while, then repaired to Shadowfang Keep, intending to use the fortress as a base of operations to fight against both the Alliance and the Horde. Packleader Ivar Bloodfang, a worgen scout, has tracked them down and enlists the help of Alliance players in order to kill them.
Horde
After Baron Ashbury, Lord Walden and Lord Godfrey were raised into undeath, they served the Forsaken for a while. However, they betrayed their newfound allies a short while later, with Lord Godfrey making an attempt on the life of Sylvanas Windrunner, the leader of the Forsaken. After this attempt was unsuccessful, Lord Godfrey and his allies repaired to Shadowfang Keep. Deathstalker Commander Belmont, a high-ranking officer of the Forsaken army, has tracked them down and enlists the help of Horde players in order to kill them.
Class Quests
Characters of all classes, with the exception of death knights, are tasked with retrieving specific materials from Shadowfang Keep. Druids must collect Moontouched Wood and Deathless Sinews, as well as Walden's Elixirs; hunters must do the same, but Godfrey's Crystal Scope is required instead of the elixirs. Warriors, paladins and rogues must collect Moonsteel Ingots and Deathless Sinews; paladins also need the Commander's Holy Symbol, while rogues must collect Springvale's Sharpening Stone and warriors the Silverlaine Family Sword. Priests and mages must collect Moontouched Wood and Ghostly Essences; priests also need the Commander's Holy Symbol, while mages must collect Silverlaine's Enchanted Crystal. Warlocks and shamans must collect Ghostly Essences and the Book of Lost Souls; warlocks also need the Tenebrous Orb, while shamans must collect Walden's Talisman. All these quests reward players with a level 20 weapon appropriate to their class.
Considerations
All quests related to Shadowfang Keep match the level required for the dungeon and reward players accordingly. Although you can also complete these quests in the heroic version of Shadowfang Keep, the rewards will be useless to you. However, you may still want to do this in order to increment the counter for the "Dungeon Quests Completed" achievement or to use the items rewarded by the quests as vanity gear.