Quest Givers with a blue question mark on top of their head give Daily Quests. You can do these Quests once a day.
Quest Givers with a green question mark on top of their head give One-Time Quests. You can do these Quests once per Character slot.
There is a Namekian with an orange question mark on top of his head, which gives Random Quests. You can do these quests anytime. The quests are completely random and make you kill 5 each of 3 different (or the same) enemies.
Quest Givers with a red question mark on top of their head are Travel Quests, or World Quests. They are for you to find an object to transport you to a different map (Namek, Space, Destroyed Future).You can do these Quests once per Character Slot. It is recommended to do these at the start of the game, because on total they give 45,000 EXP and 9,000 Zeni.
There is a unique type of Quest only available in The Secret World, called Golden Quests, or Friaza's Quests. They appear as golden question marks, and are only given out by the Universal God of Destruction Friaza. They are mainly about killing strong NPCs, and give out large amounts of EXP and Zeni.