Oxygen Meter

Oblivion
In The Elder Scrolls IV: Oblivion players have an oxygen meter which shows how long the player has left underwater. When the timer runs out the player will die.

Skyrim
In The Elder Scrolls V: Skyrim the dragonborn doesn't have a visual timer but the player will start losing health after around 20 seconds underwater. After being water all races will gasp for air.

Trivia

 * Argonians have a natural ability to stay underwater indefinitely.
 * Other races can stay underwater for longer by using spells,potions or enchantments.
 * Contrary to popular opinion stamina does not affect the time the player can stay underwater.
 * It seems the longer the player spends underwater the more frantic and deeper the breaths.