There are several ways to measure modern military power, thus it is not an easy task to rank the world navies, however there are, arguably, two exceptions to this task when it comes to the 21st Century: (1) Forward Force Projection [FFP] and (2) the ability to use a nuclear weapon against one's foe(s) on the high seas.
This type of naval ability is often referred to as a "blue water navy." Because of the grand scope of the seas, FFP involves many considerations.
Briefly, a successfully assembled blue water Armada must be self efficient; have an air force greater in strength than all land/ sea based air power within striking distance; and carry within its' floatilla "seige weapons [SWP] like the American surface fleet's horde of cruise missiles.
In addittion, a naval power must have uncalcuable preparation, battle hardened training; and the ability to land a task force of soldiers(marines) on the ground at any moments' notice.
A powerful navy posesses an extremely high moral; a powerful modern navy maintains equipment and technology that are years ahead of all possible enemies. A great navy amaintains an Academy that consistently produces great military minds. A strong navy is backed by a free society of citizens and laws. A strong navy maintains a keen level of surprise and special forces.
A strong navy, most importantly, protects the Sea Routes of Free Trade and Commerce. A strong navy is capable of miraculous action at times of human suffering by offerring relief assistance.
Finally, a Strong Navy is a powerful navy.
The current, ten most power ful navies in the world are:
1. U.S. 4th Fleet.
2. U.S. 2nd Fleet
3. U.S. 7th Fleet
4. U.S. 3rd Fleet
5. U.S. 6th Fleet
6. U.S. 3rd Fleet
7. U.K. Royal Fleet
7. South Korea