There are so many different Types of Quests in WoW:
** The most common ones involve killing certain enemies to collect certain items or simply to kill a certain number of some monsters.
** There are delivery quests that take you from place to place and lead you to new areas to explore, some of these are actually letters that you can read.
** The more unusual quests include escorting NPCs from place to place, completing some objective within a time limit and finding a particular object or location in the world.
** There are quests to defend waves of enemy attacks and quests to infiltrate fortified areas and destroy some books and other things.
** There are even quests that make use of emotes,
** There are some puzzle and riddle type quests.
** Some quests actually start from objects on the floor, and many towns have "Wanted Posters" that also start quests to hunt down some criminal. Players are rewarded for paying attention to their game environment.
(1) Strange Alliance - "Gain a Friendly reputation with the Gelkis, then speak with Uthek the Wise."
(2) Compendium of the Fallen - " Retrieve the Compendium of the Fallen from the Monastery in Tirisfal Glades and return to Sage Truthseeker in Thunder Bluff."
(3) Troll Temper - "Bring 20 Vials of Troll Temper to Trenton Lighthammer in Gadgetzan."
(4) Grim Message - "Gather Witherbark Skulls and place on Nimboya's Pike. Place Nimboya's Laden Pike at one of the Witherbark Villages in the Hinterlands, then return to Nimboya in Stranglethorn. "
There are Types of Quests which are Specific to Class or Profession, you should try to do quests of this nature as they will help you progress your chosen class and the professions you've opted for.