King of the Andals, the Rhoynar, and the First Men

The King on the Iron Throne is the ruler of the Seven Kingdoms of Westeros. The King is formally styled as King of the Andals and the First Men, Lord of the Seven Kingdoms and Protector of the Realm.

Former kings

 * Aegon I Targaryen
 * Maekar I Targaryen
 * Aegon V Targaryen
 * Aerys II Targaryen
 * Robert Baratheon

Disputed
The Throne is currently disputed between
 * Joffrey I
 * Stannis I
 * Renly I (now dead)

And also claimed by:


 * Viserys III (now dead)
 * Daenerys Targaryen

Robb Stark of The North and Balon Greyjoy of the Iron Islands are also fighting to have their respective territories secede from the realm and form their own independent kingdoms, but they do not claim the Iron Throne itself.

In the books
The full title used in the books is "King of the Andals and the First Men and the Rhoynar, Lord of the Seven Kingdoms and Protector of the Realm". Its probable that "and the Rhoynar" was omitted in Season 1 for the sake of not confusing viewers who haven't read the books with too much information, because Dorne and the Rhoynar haven't been introduced yet.