Which actual nation do Valyrians represent?

[Valens]

An ancient culture, highly developed at a time when most other countries were barbaric, where intermarriage between brother and sister was common...does it give you any clues? I'd say Egypt. Of course, their physical traits are different and had to be, otherwise it would be too many similarities and would just look banal. Andals are obviously Europeans, present day Europeans that came from the East, First Men are the original Europeans, Volantenes, Tyroshi and Myrish have Semitic traits, this time also physically. Or maybe Volantis is meant to be India? They have elephants, right?

[John Doe]

The Valyrians aren't egyptians. No people are just direct copies from rl.

[Ser Leftwich]

Nothing is a direct analog to reality. Generic, magic-using volcano dominant culture (somewhat Atlantis) with pieces from various ancient Mediterranean cultures.

[Jon's Queen Consort]

7 minutes ago, Ser Leftwich said:

Nothing is a direct analog to reality. Generic, magic-using volcano dominant culture (somewhat Atlantis) with pieces from various ancient Mediterranean cultures.

This, they don't have any real counterpart.

[Dorian Martell]

29 minutes ago, Valens said:

An ancient culture, highly developed at a time when most other countries were barbaric, where intermarriage between brother and sister was common...does it give you any clues? I'd say Egypt. Of course, their physical traits are different and had to be, otherwise it would be too many similarities and would just look banal. Andals are obviously Europeans, present day Europeans that came from the East, First Men are the original Europeans, Volantenes, Tyroshi and Myrish have Semitic traits, this time also physically. Or maybe Volantis is meant to be India? They have elephants, right?

The empire is an analog to Rome, with Ghis as an analog to carthage.  There is so much more to that though.  It is not a direct one to one comparison 

[Pain killer Jane]

They aren't direct copies but they are allusions to various empire building cultures we have seen in the real world. 
Roman Republic
Egypt (classical and post Alexander the Great)

51 minutes ago, Ser Leftwich said:

Nothing is a direct analog to reality. Generic, magic-using volcano dominant culture (somewhat Atlantis) with pieces from various ancient Mediterranean cultures.

Hawaiian culturewhich is a volcano dominant culture, practiced incest and as a part of the Polynesian culture provides us with the concept of mana (that thing that fuels magic in video games but is completely different) in relation to its affect on pono (balance). 

[Lord Wraith]

I remember reading once that Martin said Valyrians were his analogy to elves in other fantasy. So no real historical counterpart. 

[WilliamWesterosiWallace]

I'd say they're a mix of Rome, Greece, and Spain. Colonization, slavery, incessant chase for gold, a fallen society rebuilt by what survived the fall...

[Falcon2908]

United States

[siyxx]

I thought it's something partly mythical like Atlantis? Lost civilization destroyed by mother nature and all that.  

[Duranaparthur]

The immense power vacuum left over after their destruction seems most immediately applicable to the Roman Empire, but that's the biggest similarity I can see to any real world culture in terms of clear analogues. The fact that they had dragons means their  power structure was immensely more stratified than most other great empires, which tended to have an expansion of their elite to accompany the needs of militarism on such grand scales. The Targaryens resemble both the Ptolemys of Egypt in that they assimilated to the culture of their new holdings and practiced incest, but with a dash of the Plantagents and Normans who came to England. And their apparent technological superiors smells a bit more like the Assyrians than other empires.

Funny enough, they do seem like Martin taking a lot of Tolkein's framework for both the elves and the Numenoreans from Middle Earth and reinterpreting them through a far more exploitive and cynical lens, which is perfect for the story.

[Lord Wraith]

30 minutes ago, Falcon2908 said:

United States

'Merica.

[cgrav]

1 hour ago, Duranaparthur said:

Funny enough, they do seem like Martin taking a lot of Tolkein's framework for both the elves and the Numenoreans from Middle Earth and reinterpreting them through a far more exploitive and cynical lens, which is perfect for the story.

I actually get this more in the First Men, at least thematically. In LoTR, Aragorn is embodies the union of ancient magical Elves and Numenoreans, who are a semi-fallen race. Likewise in Ice and Fire, Jon Snow is a hybrid of the ancient magical Valyrians and the semi-fallen First Men. Also, they both have Sean Bean in the screen adaptation.

[Lurid Jester]

Atlantis. 

[Lord Vance II]

Totally Atlantis. Super powered, advanced civilization that colonized the world before sudden, cataclysmic end. If I remember correctly, much of Vaylria fell into the Smoking Sea, so that's even a hint. 

I know OP asked for a "real" nation, but I think it fits Atlantis well. Especially if you believe History Channel and think everything came from Atlantis. 

[SeanF]

Politically,  they have a lot in common with Republican Rome.  An aggressive aristocratic Republic, dominated by 30-40 great families vying for dominance, which subjugated surrounding nations, practised slavery on a huge scale, and at times was prepared to resort to genocide.  And fought three brutal wars with a rival imperial power, across the sea, finally resulting in that power being wiped off the map.

Their offshoot cities, such as Volantis, Norvos, Qohor, were like Greek colonies.  They were autonomous, but retained ties with the mother city, and could call on the mother city for aid in time of war.

[Lord Vance II]

5 minutes ago, SeanF said:

And fought three brutal wars with a rival imperial power, across the sea, finally resulting in that power being wiped off the map.

Valyria salted Ghiscari farmland just like the Romans did the Carthaginians, right?

[SeanF]

6 minutes ago, Lord Vance II said:

Valyria salted Ghiscari farmland just like the Romans did the Carthaginians, right?

That, too.

[Protagoras]

37 minutes ago, SeanF said:

Politically,  they have a lot in common with Republican Rome.  An aggressive aristocratic Republic, dominated by 30-40 great families vying for dominance, which subjugated surrounding nations, practised slavery on a huge scale, and at times was prepared to resort to genocide.  And fought three brutal wars with a rival imperial power, across the sea, finally resulting in that power being wiped off the map.

Their offshoot cities, such as Volantis, Norvos, Qohor, were like Greek colonies.  They were autonomous, but retained ties with the mother city, and could call on the mother city for aid in time of war.

Not to mention that they speak of Old Valyria with implications like we do today about its impact on western culture and its historical significance.

Yup, this is as clear & obvious in the same way its clear that Volantis is Constantinople. 

[SeanF]

42 minutes ago, Protagoras said:

Not to mention that they speak of Old Valyria with implications like we do today about its impact on western culture and its historical significance.

Yup, this is as clear & obvious in the same way its clear that Volantis is Constantinople. 

The Valryian attitude towards religion resembles that which Gibbon attributed to the Romans;-

"The masses thought all religions were equally true;  the philosophers thought they were equally false;  the magistrates thought they were equally useful."