Prince

Prince is a title held by the members of a ruling family, usually the royal family. Its female equivalent is Princess.

House Targaryen
During the rule of House Targaryen, all members of the royal family, except for the King and Queen, held the title of Prince or Princess.

The heir to the Iron Throne held the title of Prince of Dragonstone, and ruled the former seat of House Targaryen, with the noble houses sworn to Dragonstone as vassals.

Targaryen Princes and Princesses

 * Princess Rhaenyra Targaryen
 * Princess Daenerys Targaryen
 * Prince Baelor Targaryen
 * Prince Rhaegel Targaryen
 * Prince Aerion Targaryen, who killed himself by drinking wildfire
 * Prince Aemon Targaryen, who renounced his title and family ties to become a Maester and later a brother of the Night's Watch.
 * Prince Duncan Targaryen, who perished during the Tragedy of Summerhall.
 * Prince Rhaegar Targaryen, who perished during the Battle of the Trident.
 * Princess Rhaenys Targaryen, murdered during the Sack of King's Landing.
 * Prince Aegon Targaryen, murdered during the Sack of King's Landing.

House Baratheon
During the rule of House Baratheon, however, only the offspring of King Robert Baratheon held the titles of Prince or Princess. Meanwhile, his brothers, despite being in the line of succession didn't held the titles.

Baratheon Princes and Princesses

 * Prince Tommen Baratheon, current heir to the Iron Throne.
 * Princess Myrcella Baratheon, second in line to the Iron Throne.
 * Princess Shireen Baratheon, heir to claimant King Stannis Baratheon.

House Martell
House Martell still rule Dorne as Princes. The head of the family holds the title of Prince of Dorne - or Princess in case of female rulers - while the rest of the family hold the titles of Prince or Princess.

Martell Princes and Princesses

 * Prince Doran Martell, the ruling Prince of Dorne and Lord of Sunspear
 * Prince Trystane Martell, the youngest son of Prince Doran.
 * Prince Oberyn Martell, Prince Doran's younger brother.