Ahh...the Dunedain. Now, someone correct me if I'm wrong. I'm bound to get a lot of this screwed up. Here's a short version of how they came to be.
[sblock]Basically, the Dunedain were named after the Edain, who were named after a Man of the same name. He was the leader of a House who became friends of the Elves (the Noldor, I think) during the First Age. The Elves taught them much. The Edain and the Elves did much to contain Melkor's evil during the first age. Melkor, for those not in the know, was basically an Evil God in Middle-earth. Sauron was his minion.
Not that the Edain were immune to being evil themselves, mind you. There are stories of evil men even among them, but they were pretty much humans who befriended Elves. They were no better than other humans, except that they were taught by the Elves.
The First Age ends and a crapload of Men die in the final war against Melkor.
Of those who remained true to the side of Good and still lived(bec. many more Men flocked to Melkor's side), they were given an island to the West. And they founded the kingdom of Numenor. It was an Atlantis of sorts. The Numenoreans were gifted by the gods (the Valar) long life, though they could not take away death (since it was Eru's, the Uber-god, "gift" to the race of Men). So they became long-lived and wise. They were taught more stuff by the Elves. Blah blah blah.
From time to time, Numenoreans returned to Middle earth to help out and teach the other humans who remained behind then go back to Numenor. They were seen as gods by these folk.
And then things turned to crap. The Numenoreans began to lust for immortality. They began to obsess over death. A small number of them remained true and good. But even their line of Kings became mostly evil and tyrannical. They began to rule over the coasts of Middle-earth and demand heavy tribute from those they once helped. This was in part due to Sauron the deciever who came to Numenor to corrupt it, but the seeds of evil were lain long ago.
So the Numenoreans do something momentously bad (they try to sail to the home of the Gods to gain immortality). And Numenor sinks. Fortunately, a few of the good Numenoreans survive. They go to Middle-earth and establish Arnor and Gondor. Stuff happens, the Last Alliance of Men and Elves attack and defeat Sauron (who managed to escape Numenor's doom).
End Second Age.
Arnor falls to ruin. Gondor, almost the same, but manages to survive somehow. But the Numenorean blood in Gondor is diluted, so the grace of the Valar is lessened with every generation.
The Numenorean blood in the Dunedain is more pure but they are very very few. I forget how the Dunedain get their name EXACTLY. But they're all that remains of the line of Kings from Numenor and they protect the lands around the Shire against the Enemy [/sblock]
I dunno if they're meant to rule other races, but they tend to be wiser than others (Denethor craziness nonwithstanding). I think that they believe themselves fortunate in the same sense that many well-off people think themselves fortunate compared to those not so well-off.
They're still Men. And in Middle-earth, Men have a tendancy toward corruption, even the Numenoreans. For example, the Mouth of Sauron is a Dark Numenorean.
Of course, they have super powers, too. Super vision (but not as good as an Elf). Endurance. Wisdom. An aura of majesty. Blah blah blah.
Like the other posters, I would use Aasimar stats for them except to say that they're still Human rather than Native Outsider. Or, as Dr. Ackward mentions, Human Paragon fits the bill (for a race of High Men, not Dunedain, exactly).
With that LA+1 in place, no one will want to play them. HA!
