Daily quests (popularly nicknamed dailies) are repeatable quests first introduced in patch 2.1. These quests have significantly better rewards than normal repeatable quests. Patch 2.2.0 saw the introduction of more daily quests for seasonal events. In Patch 2.3 new daily quests were introduced for instances, battlegrounds, fishing and cooking.
You may complete up to 25 daily quests per day per character. The exact reset hour depends on the realm, but it never changes, is chosen to be in the early AM, and will not coincide with the instance reset. You can double-check by mousing over the daily quests completed out of 25 in the upper-right corner of your quest log. Prior to Patch 2.4 there was a limit of 10 daily quests per day, but was increased to the current limit to accommodate the large number of Shattered Sun Offensive daily quests.
Often, a quest chain needs to be completed first to unlock the quest. All daily Skyguard, Ogri'la, and Netherwing quests require level 70 and require a flying mount. Netherwing daily quests require the artisan (epic flying) riding skill, although not an epic mount. The Cooking and Fishing dailies require level 70 to obtain, but only a few require that you be able to get to places which require flying.
There are a maximum of 45 daily quests available to a player at any one time (when all have been unlocked). This does not count seasonal events.
Below is a list of all daily quests ordered by faction and location.