Comments.
c.400 - c.453: Hunnic Empire
Date quibble: The Hunnic Empire in its quasi-centralized, world-conquering, Roman-beating form really can't lay claim to existence until the late 430s (exact date unknown, natch) when Aetius let them settle on the Pannonian plain in exchange for helping him fight the Burgundians.
taillesskangaru said:
c.453 - 636: Byzantine Empire, Sassanid Empire
Tsk tsk. The Sassanids were at no point - save perhaps the Romans' nadir in 610-22 - stronger than or even equal to the Empire. The Eastern Romans consistently fought them off or even expanded, while at the same time conducting campaigns in Africa, southern Spain, and Italy. Compare the two: all the Sassanids control is the relatively desolate Iranian plateau, plus Mesopotamia, which is the economic and cultural heart of their empire. Eastern Rome has Anatolia, Egypt, the Levant, and the Aegean littoral, and adds populated territories like North Africa and most of Italy later in the period. It's instructive that the Sassanids only scored a temporary success against the Romans when a) allied to another power (the Avars) and b) faced with internal Roman dissension and uncharacteristically poor leadership at the top. Immediately before Khusrau's great march of conquest that ended at the Propontis, he'd had to be put on the throne by a Roman Emperor, and part of the reason he invaded the Eastern Roman Empire was to get revenge for his benefactor's death at the hands of a usurper! (Conquest played a big role too of course.

)
taillesskangaru said:
c.800 - c.1000: Abbasid Caliphate, Vikings, Byzantine Empire
Speaking of the Vikings as a single entity is IMHO a poor plan, of course, but I suppose the wording of the original question is flexible enough. In addition, there should be an additional demarcation, indicating Roman superiority over both of these from about 867ish, which marks the beginning of the Macedonian dynasty and a general roll-back of Muslim gains, to 1071.
taillesskangaru said:
c.1000 - c.1200: Song China, Seljuk Turks
I'd put the Seljuqs as starting their stint at 1071 (since in the campaigns before that Romanos had actually beaten Alp Arslan multiple times and driven him out of the Empire) and ending with the death of Malikshah I in 1092, because at that point Great Seljuq split up into multiple successor states, none of which was terribly powerful (and the most well led of these, the Sultanate of Rum, lost ground in the next hundred years to the Romans before finally being put out of its misery by the Mongols).
taillesskangaru said:
c.1400 - c.1450: Ming China, Mamluks
I wouldn't really rank the Mamluks so high. Outside of their own dominions, I can't recall them being able to significantly project power during this period. They certainly weren't well off enough to intervene in Anatolia after the Battle of Ankara to take advantage of the Ottoman weakness.
taillesskangaru said:
c.1500 - 1550: Portugal, Spain, Ottoman Empire, Safavid Persia, Ming China
Now that's getting away too easily.

Putting in multiple Powers in a given timeslot is okay up to a point, but eventually you stop going from "compromise" to "wishy-washy" and "unable to make a decision".
Portugal does retain significant commercial power over Spain in southern Africa and the Indian Ocean, that's true, and said commercial power is nearly total in those areas. But the Habsburg dominions combined, I think, would outweigh the Portuguese by a significant factor. When all's said and done, the Portuguese economic monolith during this period is based on an awfully small population and an almost depressing inability to win on the land, especially if they were up against the Spanish. The Safavids, too, are clearly inferior to their Ottoman Turkish neighbors, what with losing at Chaldiran and generally being on the back foot against Suleiman and Selim. At the most, I'd say that you could split this between the Habsburgs and the Ottomans and the Ming, and perhaps even drop the Ming; that Empire's golden age was the 15th century, and it is already starting to go downhill.
taillesskangaru said:
c.1550 - 1600: Portugal, Spain, France, Ottoman Empire, Safavid Persia, Mughal Empire, Japan
Portugal during this period is partly in personal union with the Habsburgs, so they're out. France would be better suited to the previous period than this one; they begin it with military defeat and the Peace of Catteau-Cambresis, and they go through decades of religious issues, with interventions on the part of the Habsburgs, until finally shaking off the confessional and Habsburg struggles under Henri IV at the tail end of the period. Definitely not in the top seven, much less the "most powerful". Spain is a gimme up to about the Treaty of the Pyrenees in another fifty years, so they're good. Ottoman Turks are reasonable I guess. Safavids are doing even worse now than they were earlier, with new defeats at Suleiman's hands in his old age (I think we can all agree that Tahmasp just sucked at life), although they do revive under Abbas at the end of the period to some extent I would place them in the first rank
maybe in the next fifty years, not this part. The Mughals are probably okay. Japan is an interesting choice, but for most of this time they were internally focused and not really united, and in their sole appearance on the international arena as a single entity, the Korean campaign, they suffer defeats on the sea and have their little adventure rapidly terminated. I probably wouldn't go with them here either.
taillesskangaru said:
c.1600 - 1650: Portugal, Spain, Netherlands, France, Britain, Ottoman Empire, Safavid Persia, Mughal Empire
Portugal doesn't get out from under the Habsburg thumb until 1640, so they're out again. The Habsburgs are again a gimme, but this is the last time. The Netherlands are GA'ing right now, so they're good. France is an interesting choice, but in my opinion right now they're not really superior to the Spanish one-on-one until after they formalize it with the Treaty of the Pyrenees. Up to that point, the French were able to rely on other Powers to keep the Habsburgs worried about another area (like the biggie, of course, the Swedes); after the Treaty of the Pyrenees, Louis XIV goes it largely alone and ends up winning most of the wars anyway. So I'd defer France for another fifty years. Ottoman Turks are in their last real possible half century for this, and they're still huger than most everybody else, so they're in. The Safavids hit their one possible Great Power stride right here, although notably they are in large part dependent on Western arms and economic aid to successfully struggle against the Ottomans under Abbas. Mughals also might be up there as well.
So that little "winnowing" bit didn't really eliminate most of the choices during the 1600-50 period. If I had to choose one of them, it'd be the Habsburgs though. They do an excellent job holding their own against opponents from all corners of Europe and Asia, including some of the others mentioned here, and still retain a largely unchallenged and vast empire in the Americas. That personal union with Portugal until 1640 also gives them access to the Portuguese Network of the Three S's (spice, sugar, slaves) and commercial supremacy unchallenged by anyone save the Dutch (who really, really do well at this point in time, but in a one-on-one against the Habsburgs would have been utterly annihilated).
taillesskangaru said:
c.1650 - 1700: Spain, Netherlands, France, Britain, Ottoman Empire, Mughal Empire, Qing China
Spain's out. The Sick Man of Europe doesn't get to be in the top group anymore.

The Netherlands might be in, although this is mostly based on the end of the period when they briefly have a union with the English and Scottish thrones (i.e. Britain) under William of Orange. France is definitely in the top group. If they were on top of the world at any point in time, it's now. The Brits are largely out, I think, because they really don't flower until the very end when they're bolstered by the Dutch. Ottoman Turks are out. They lost at Vienna and ended up being ejected from Hungary and the Morea as well as other random enclaves that the Venetians wanted. Mughals are out, too, I think; despite the external expansion that Aurangzeb is famous for, that new territory didn't stay in Mughal possession that long, and he was never able to subdue the Marathan Confederacy of Shivaji and his successors. The Empire of the Great Qing, I believe, wasn't the same kind of powerful Power that the French (who IMHO are on top completely) at this time. Their navy is practically nonexistent and outside of China Proper and Manchuria they have basically no power projection. Europe has also already begun to overtake China technologically. So while the Qing are quite a strong country at this juncture, IMHO France is doing better.
taillesskangaru said:
c.1700 - 1750: Spain, Netherlands, France, Britain, Austria, Russia, Qing China
Spain's out. Netherlands are past their prime, they're out too. Russia hasn't really come into its own yet on the world stage and won't until the Napoleoni Wars. Qing China maybe, but they really haven't gotten much better than the last period to the best of my recollection (vis-a-vis the Brits and French anyways). Austria is doing OK for the most part but they lose a little to the Turks and a lot to Fred II from Prussia and I wouldn't give them the top slot. I personally would divide this between the French and British, with the French having predominance after 1745 and the British having predominance before that time. Fontenoy was sort of a turning point, a reversal of Marlborough. And France clearly outdid the Brits in the War of the Austrian Succession in general. We won't see a sea change between the two until 1759 IMHO.
c.1750 - 1815: Spain said:
Spain's out. France loses the title to Britain in 1759 because of losses in India and at the Plains of Abraham. They then get it back in 1793 as they mobilize for the Wars of the French Revolution, and keep the title until 1813 when Boney loses the Battle of Leipzig and his last chance to retain his Empire's supremacy over Europe. The UK then takes up the slack once more, what with their unchallenged global colonial supremacy, although Russia is probably more powerful within Europe itself. Prussia is a tiny weakling for most of this period and doesn't really even deserve mention - their greatest successes during this period were "surviving" and "taking a big bite out of Poland with some help", the first of which doesn't say "most powerful" to me and the second of which is against
Poland, for God's sake.

Austria loses ground during this period with the sole exception of the acquisitions of Venice and part of Poland, the first of which they eventually lose entirely and the second of which is virtually dismembered and unrecognizable by the end.
taillesskangaru said:
1815 - 1860: Britain, Austria, Russia, Prussia
Despite the
Zollverein, Prussia is an economic midget during this period and really doesn't come into its own until about 1860 or so with the accession of von Bismarck and the passage of the new military laws that finally restructure the Heer into something that makes sense. Austria doesn't even manage to enforce the Vienna settlement with help, much less without it. Russia is supreme in Europe until 1855 and the fall of Sevastopol, while France is "win" after that; Britain in the larger world retains overall supremacy, however, because they really have no competition.
taillesskangaru said:
1860 - 1870: Britain, Austria, Russia, Prussia, France, United States
Britain, yes. Austria, no: they go from defeat to defeat during this period and just overall exhibit that trend of Franz Josef's reign which can only be referred to as SUCK. Russia is still recovering from the internal shakeup that the Crimean War precipitated and really isn't ready to do much of anything. Prussia and the NGC are definitely extremely powerful at the end of the decade, but until then France still retains more diplomatic weight and prestige, and while French armies ultimately fail in Mexico they are still regarded as being on the technological wavefront and are better than anything Prussia has, save for Prussian artillery. (Chassepot > needlegun.) And finally, we have the United States - which, I firmly believe, was, in 1865 upon the defeat of the Confederacy, due to the mobilization of its industries and populace, briefly the most powerful state in the world. They had a navy comparable with the Royal Navy, which was in the throes of reorganization; their army was larger than anyone else's, even Russia's, and was battle-hardened and equipped with fairly modern weaponry (missing the needle-gun development by an ace, and equipped with those awesome cavalry carbines and an absolutely fantastic artillery corps). Oh yeah, and everywhere outside of Europe and America, guess who's strongest? It's still the UK, though their dominance will start to erode soon.
taillesskangaru said:
1870 - 1918: Britain, Austria, Russia, Germany, France, United States, Italy, Japan
The Brits are clearly in the top group at this time. Austria-Hungary continues to fail and doesn't get much better than what they lost to France and Prussia with years earlier. They also end up losing. Russia, in the time-honored tradition of sloppiness that is its national character, has economic growth that in percentage terms looks nice, until you see a) that in absolute terms it's not that much and still a pygmy compared to the UK, US, and Germany (and even France IIRC) and b) the social issues generated by said growth were enough to tear the country apart with a global conflict as the catalyst, because in addition to shoddy development, Russia faced the problems of poor leadership and a low-quality army during this time. Their only real success was in conquering Central Asia under ma boy Skobelev, which, while impressive on a map, really didn't add much in terms of actual power. France is clearly eclipsed by Germany in all manners save perhaps liquid capital for investments, which while fairly important doesn't win wars. In France's case, she had the good ("good" here meaning "better") set of allies, which made all the difference. Italy is a piece of junk country compared to the rest of Europe and doesn't deserve examination. Japan, while doing a very good job of modernization, isn't even a Great Power yet, much less one of the top group. And the United States is militarily inferior to most of the European participants in WWI, although its economic growth is, like Germany's, staggering. So I'd call this period an age of Germany and the UK.
taillesskangaru said:
1918 - 1935: Britain, France, United States, Japan, Soviet Union
France and Britain are doing pretty badly during most of this period, only retaining a veneer of supremacy over the fact that they almost lost the last war and are completely exhausted from it. It gets so bad that they have to turn to Socialism for awhile to recover from it and from the terrible condition of being subject to the economic vagaries of the true power during this period, the United States. The Soviet Union are in the middle of modernizing and slaughtering their own inhabitants and aren't really up for consideration. Plus, I mean
come on...when the Poles beat you, you're really screwing up. So it is the United States' economic muscle and Japan's military might that dominate this period.
taillesskangaru said:
1935 - 1945: Britain, Germany, United States, Japan, Soviet Union
The Brits are doing okay, I guess, but they're definitely not on a par with the US, Japan, or the Sovs. Germany only really is good during the period 1938-43, from Munich to Kursk, and before and after those points the Soviet Union and the Americans are superior to them. Japan is probably doing the best of anyone up to 1938, with a battle-hardened army and a slew of new resources from China, and the Germans are definitely on top until Kursk. I'd have to say that the joint US/Soviet slot starts here and doesn't stop until 1985-7 somewhere. Britain and France are nonentities after this, without the economic or military base to compete; they're basically just figureheads and will quickly be dominated culturally, militarily, diplomatically, and economically by the two giants bestriding the world to their east and west.