Aegon I Targaryen forged the Iron Throne from the swords of his conquered enemies, and it is the ultimate symbol of power in Westeros.
Robert I Baratheon became the first non-Targaryen king to sit atop the Iron Throne when he rebelled against the tyranny of Aerys II Targaryen.
Joffrey I Baratheon ascended to the Iron Throne after the sudden death of Robert I Baratheon during a hunting accident. Despite his youth and short reign, Joffrey earned a dreadful reputation and many enemies during the War of the Five Kings.
Daenerys Targaryen claims to be the legitimate heir of the Iron Throne. From across the Narrow Sea she plans her invasion of Westeros with her 3 dragons, but whether she eventually sits on it remains to be seen.