Are the Pillars of Argonath supposed to be particular kings, or generic Numenoreans? Also, why are they there? There’s no ancient cities nearby – Amon Hen is just a watchtower.
They’re pillars carved with the images of Isildur and Anarion, and they mark the northern border of Gondor.
They are in the likeness of Isildur and his brother Anarion, sons of Elendil. The two brothers founded Gondor, and ruled over it jointly. Isildur in Minas Ithil (later Minas Morgul) and Anarion in Minas Anor (later Minas Tirith). They had a palace in the capital city of Osgiliath. Two thrones were set side by side there, at equal height.
Meanwhile in the north, Papa Elendil founded Arnor. He was acknowledged as High King of both Arnor and Gondor. When he fell, Isildur the elder son took up the high kingship of Arnor and Gondor, and committed the rule of Gondor to his nephew, Meneldil. Anarion had been slain during the siege of the Barad-Dur, prior to Sauron coming out to do battle personally.
IMHO, PJ took some liberties with the Argonath in the movie, to make them look more like father and son, Elendil and Isildur. But that’s not how JRRT had it.
There. That’s probably more than you wanted to know.
::points up:: I knew he’d be along shortly. 
I love this place. Deep definitive answers in the time it takes to walk my dog.