1. United States of America
The US military is undoubtedly the most useful military institution. It is expansive, dominant, precise, powerful, and capable of projecting power globally, on multiple fronts. It is incredibly effective at compelling foreign polities to be more friendly and useful to the United States, and protects the American economy through global stability, and stability within key extraterritorial regions. Not only that, but it allows America to vanquish its adversaries without major casualties, enabling military intervention in extraterritorial, "detached," conflicts (Republicanism and Democracy are intrinsically opposed to the use of military force). Essentially, America can eliminate whoever it wants to, wherever it wants to, and without perilous attrition. The United States military is an institution that is instrumental in executing American interests.
2. Israel
The Israeli military is also a very beneficial institution. In fact, it is the single most beneficial Israeli institution, and the one organization that enables Israel to exist. It has proven itself, through multiple wars against superior opponents, to be among the most effective and efficient militaries. Its success and capabilities have resulted in formal recognition of Israel throughout the Arab world, and deter Arab aggression and invasion. Israel's military continues to provide an extensive array of services that (both actively and passively) it uses to advance its national interests - it's military is much more effective in this regard than any other country (except, perhaps, for America).
3. China
Although I list China here, it is more of a future tool than a current one. However, due to its ongoing reformation, and the extremely pragmatic goals it aims to achieve, it will probably become one of the most effective guardians of any nation's strategic interests. China is aiming to amass enough force by Taiwan to put serious pressure on the island, and in the future may have some success in utilizing it to benefit China. China has also recognized its future threats and competitors, and is shaping its military to counteract them. More specifically, it recognizes that the US will be a serious competitor, and potential adversary, in the future. In response, it is building an arsenal that includes many systems tailored towards penetrating American weak spots. China is building and reforming its military so that, in the near future, it will be an extremely effective tool for use in advancing the PRC's national interests.
4. Japan
The JSDF is the dark horse of the international military stage. It does not draw attention to itself, and yet is one of the most well equipped and well funded armed institutions in the world. It has a military outfitted with proven equipment that has been upgraded to be superior. It is well trained, and is extremely proficient at territorial defense. Existing in a region that is only tentatively stable (with China, America, and radical Islamism all fighting for supremacy, and the last vestige of militarist communism making ever bellicose threats) demands a strong military, which Japan has. But not only is Japan virtually impregnable (worthy alone to be on the list), but it has also begun to show a willingness to use its forces abroad, and become proactive on a global scale. This will surely translate into more martial use in promoting its national interests.
5. Iran
Iran has an often ignored defense establishment, so one may wonder why it deserves such major mention. Iran is a major sponsor of terrorism against the US, an "official" enemy of the US, and is engaged in war against America. It subverts American interests at every junction, and is one of the biggest impediments to the realization of American domestic and foreign security. Logically, it follows, America should eliminate Iran. However, Iran has a very impressive military for defending itself (and it's a very hard target to hit). Iran's military strength protects it from American invasion and heavy military retaliation. It's military, like Israel's, realizes the nation's ultimate moral purpose: advancing the interests of its citizens. However, unlike Israel's, it is not as proactive. Ergo, it is number five, and the IDF is number two. Regardless, Iran's military is one of the finest at advancing its national interests.
6. Britain
Britain has a well balanced, well funded, powerful military. It is capable of deploying force and projecting power to advance London's interests, and is more powerful than any force it will likely face. That said, it is certainly not the world's powerful. So why put it at number six? For political reasons. Because London is willing to employ the British military to advance its strategic interests, it makes the military that much more useful. The royal armed forces can be and are employed in defense of Britain, in offense against Britain's enemies, and to advance its national interests.
7. Australia
See above.
8. Singapore
Singapore is a small nation with a small military, true. However, they take their defense very seriously. See the comments about Japan to understand the gravity of their situation. Therefore, since they take defense so seriously, their military is very effective in promoting their national interests. It is efficient, well trained, and very capable of defending Singapore. This combination of efficiency and employment give it such a high spot - rightly or wrongly, Singapore believes that they need a (relatively) powerful military to defend their city-state, and it is extremely effective at doing so.
9. Pakistan
Pakistan has a powerful military, which they use (along with the ISI) to effectively control the region. Pakistan's military has been employed to good effect to advance its national interests, and thus earns a high spot.
10. Republic of Korea
The RoK has a strong military that is built around their most compelling national interest - to defeat a potential DPRK attack. Because the military satisfies this condition fairly well, they earn a spot on this list. However, due to political sentiments (that have begun to appear) that are apprehensive and opposed to using the military as a tool of advancing their national interests, South Korea's military is relegated to tenth.