It is quite common to hear of the "emerging powers" in various global news sources. So let us look at which nations have been granted this distinction, and whether or not it is fairly applied. This list is based on various news or scholarly articles listing these nations as such. So, let us now begin with those so designated:
Brazil - I take big issue with this designation. In 1987, Sarney said they would be nuclear by the start of the 21sr century. As we all know, they disarmed, and now only have a modest nuclear energy program. Rumors that they may have covertly re-started weapons development appear unfounded. They have the 18th largest army in the world, but only through conscription. Only 37% of airforce planes are operational, and a full 60% are over 20 years old. Only 10 of 21 surface ships are operation to patrol their 7000km coastline. They only have 1 (of 5) fully operational submarines. And 54% of helicopters don't work. Most land vehicles (~80% now) are over 30 years old, and only 20% are combat ready. In other words, they are militarily a joke. By total GDP, they have the seventh largest economy. Taxation and excess governmental involvement, coupled with reckless liberal spending, is hurting th economy on the whole. And the standard of living generally sucks.
China - I think there is no doubt that China is a power, or for that matter a new super power. They have the world's largest population (but India will eventually win there), a nuclear arsenal, large labor output, and extensive investment in foreign countries. Plus, their currency is sufficiently free floating at the moment that they can manipulate the market into even more favorable terms. If they got rid of this communist non-sense and fully embraced capitalism and human rights, they could become the new hegemon. Luckily for the US, this seems unlikely.
India - Again, no clue how anybody can question this one. They have roughly 1/6 of the world's population, and will overtake China for the #1 spot by 2050. They have a vast nuclear arsenal, and a right wing that is all too happy to use it. Based on a long standing conflict with Pakistan, and the status issues for Kashmir, they have incentive to keep developing new weapons and expand the military. Their economic realities of the average person outside of major cities is an issue. And the laws need to be harmonized more, as right now you'd swear it was several countries. But they are becoming a major hub of technology. And the wide understanding of English makes them a powerful business center.
Indonesia - They are extremely unstable. Aceh has calmed for now, but who knows when that will end? There are still active separatist movements across the country. And they have no problem using violence. Outside of that, the large Muslim population contains within it a massive number of fanatics interested in taking over and enforcing sharia law. GDP PPP is lower than Brazil's, with 18% living below the poverty line, and roughly half (49%) living on less than $2 US (Rh. 20,000) per day. Overall, internal political turmoil, Islamist elements, and an unimpressive military means it won't become a world power.
Japan - I think this is fair. Their constitution forbids active deployment of troops, but many politicians within the dominant LDP want to change that. And if they do, their forces would be damn significant. Nuclear status is questionable, but could easily be reached if it has not yet been. Excellent economy and a very stable government. Huge population, strong networks, and quick adoption of new technologies is also good. The currency scare of the 90's was a major blow, but I think Japan is starting to exit the slump. It would do well to amend the constitution and strengthen ties with South Korea. But generally, this is one of the fairest applications of the "emerging power" label
Mexico - We have over 10 million of them who came here by crossing the border illegally. That alone should indicate they are not a world power, but a hellhole people generally want to leave. It is true, they now have the world's richest man, but one man doesn't make a nation. Their military has potential, but is underfunded and underarmed. No chance of them going nuclear any time soon. Rich resources cannot make up for widespread poverty.
Nigeria - Nigeria is split, which several states practicing sharia law. Religious tension is the defining internal issue. They are stable by African standards, but not by general ones. And the fact that North Korea is a major supplier to them will hinder greater economic internationalization, which is needed to strengthen the country. It his the headquarters of 419 scammers and has the second largest population of people living with AIDS. In other words, even if they had an impressive military and economy (they don't), they would have a long way to go before even making the list as emerging.
Russia - I take issue with this one, because I believe it has been since World War II. I don't think the fall of the Soviet Union created true unipolarity. Rather, Russia was humiliated, on so remained relatively dormant. Present leadership, whatever we might think of it, has done much to restore Russian pride. They are starting to counter the US on many issues, and are manipulating their economic and political standings to do this. Until they can afford to maintain their aging weapons, and crush the Chechnyan terrorists, there will be some hurdles. But every nation has them. I maintain that it is a world power than has some domestic issues and a need to strengthen its economy. And on the latter front, they seem to be doing that.
South Africa - This is another one I take big issue with. They have the largest AIDS-infected population in the world. The fact that about 1/3 of pregnant women are HIV-positive doesn't help either. Alcoholism, also common among pregnant women there, is another lingering threat. It is too linguistically divided, with 9 recognized languages being spoke by only 80% of the population. As seems to be the African standard, poverty is very widespread. As per the military, the biggest illustration of their lack of power is the fact that they disarmed in the early 90's before the ANC came to power. Their increased military investments on hardware are impressive, albeit irrelevant. This is because in the post-apartheid era, they have had an issue finding qualified military leadership, naval combatants, and airforce pilots. So, like Nigeria, they are a regional power, but only because they are in such a piss poor region. In the post-colonial era, it does not have a serious chance at becoming a world power.
Turkey - For a Muslim country, efforts to combat religious extremism are impressive. However, their "Insulting Turkishness" laws, and the prohibition against recognizing the Armenian genocide are a little worrying. Education is not yet sufficiently widespread, especially for girls. They would gain alot from joining the EU, but they will be blocked. Recognition of the TRNC while at war with the PKK over Kurdistan is hypocritical, and hurts their image as a serious diplomatic and pragmatic nation. And since they lack the military to otherwise become a serious voice, it seems that Turkey will be a moderate Muslim power at the very most.