We're certainly the most influential, most culturally important, (debatably) the wealthiest, have the strongest military, etc. so if you use most important country in the world as a stand-in for greatest, we're undoubtedly number one.
We're usually at the forefront of global social change. When it comes to multiculturalism and rights/general acceptance of minorities, we're probably number one--at least among countries that matter.
No bloc in the world rivals the general scale of our general prosperity and freedom. When you compare the USA against Europe or East Asia, you aren't just comparing Massachusetts to Switzerland. You're also comparing Kansas to Moldova and North Korea. There's no other area in the world with 330m people that can match our standard of living.
Finally, who could actually rival us for the slot? Germany, maybe? France? Japan? There aren't a lot of obvious competitors.
China would be the obvious one. It could match the US on several aspects in the medium or long term; notably I imagine would be GDP. Possibly military too; or at least in terms of being involved on foreign interventions.
Of course it would still fail in most other aspects. A comparison could be drawn to the Soviet Union during the Cold War
