additionally, throughout history, a nation's military might, or power as you're referring to in the OP, is a reflection of and direct extension of it's economic power. While these two aspects of a nation's overall health and world influence do not rise and fall in exact proportion to one another, they are fundamentally tied together and do, over time, exhibit direct consequences on each other.
This link:

http://www.newser.com/article/d9pjkt4o0/us-falls-to-5th-slot-in-economic-competitiveness-survey-swiss-stay-on-top.html

is to a recent article concerning America's economy in relation to other countries. As our economic competitiveness wanes, so will our influence, i.e., respect, perception among other leading nations.. and eventually, our military might.

This is what I think most people mean when they talk about the decline of US power. Its not really a decline of US power per se. Its just that other countries are gaining more power and are gaining it faster. Just think of it like a pie graph where the accumulated power adds up to 100%. Emerging nations have just increased their share of the slices, and this has been at the expense of the United States.

I would also add that I feel that the BBC is anti-American, just from watching it

But the USA is facing issues, but I think it can overcome them if it sorts out its politics, I don't think anything can really get done until there is a stable presidency, where the president actually has control

US is certainly still the sole superpower. China has decades to go (or if they were willing to swallow it, a single decade of very large-scale mobilization, but that is unlikely) before they can start reaching anywhere outside of East Asia in a significant way (though they have inroads in African countries like Sudan and Angola, and retain ties to Cuba), and as others have stated, there has never really been a time when one military superpower was so far ahead of everyone else. Even in the days of British hegemony (before Bismarck or Napoleon III), though they had a lock on global naval power, they did not couple that with the kind of technological lead on their closest competitors like we have today.

Russia's military is still ahead of China's technologically, which should say something about just how far back China is, since we have a pretty fair estimate of how far back Russia is. Anyone else with competitive military technology is firmly in our bloc, and that's the end of the story

Economics is another story, but even if we in the USA can't get our shit together there, the only thing keeping China's real-estate bubble from popping is corruption and sheer willpower (e.g. the Party Men won't let the bubble pop, though it likely should have by now)

Not as onesided....

but still pretty onesided.  Assuming we're taling covnentional warfare, since nuclear warfare would just mean everyone loses, just some people lose harder.

Anyway to handle them one at a time.

1) The Chinese.  They lack force projection.  A war vs China would basically involve the US invading and the chinese defending, and that's it, because the Chinese have no way to get any of their troops to the US.  There navy would get handled fairly quickly and it'd devolve into a case of America bombing China until China gives into US demands, or America stops bombing china due to it's people getting sick of the war.  You could technically call the 2nds a chinese victory, but I mean, considering the destruction to china's economy and basically no real effect on the US, it'd be quite the phyrric one. 

2)  The Russians.  Not as powerful as they were when they were the USSR, and are actually falling behind the chinese in some military technologies, not enough ports for force projection or a good enough economy to handle the war.

3) EU.  Well to start with, the EU is a bunch of different countries.  So despite having a larger armed forces.  I think it's like more then double the US size... it would be fractured as the EU countries squabbeled over what actions to take, where to defend, and whose forces should be sent to die where.

They can't even agree on a unified fiscal policy afterall.  Outside that, there techonology is a step behind the US with a lot of the best stuff coming from the US.  Note how the EU called in the US to fight their war in Libya for them having the US send in their planes and rockets to take out all the anti-aircraft defenses before they took over airspace.  It's even more telling that Obama agreed to it, when if anything the last thing he wanted to do was get involved in another war in the "Middle East".  (Northern Africa counts.)  Afterall, Libya was basically nothing more then a more competantly done Iraq.  Basically what that tells you is... the EU wasn't confident that it could take out all of Libya's anti-aircraft weaponry without losing a plane.

The EU would have to get organized, basically agree on one military leader and then go out of it's way to reequip and retrain most of the Europeon Union army.  It'd be a logistics nightmare...

and that's assuming that the UK doesn't take one look at the situation and decideto sit out to avoid the political and military unitedness that they've already avoided when it came to the Euro.

The UK is by far the most valuable country in a US vs UK war because of the UK's outstanding navy.  If the UK went nuetral or even swtiched sides... it'd be all over.

It'd probably be the hardest challenge, but it'd probably be a lot less trouble them most would think.

you said it best yourself, it wouldn't be as one sided, but they could at least defend and counter attack with some success, unless, like you said, either sides used nuclear weapons, but if that happens, there isn't any winners

I think such comment is mostly directed at the current state of the economy. (Other countries rising fast such as China, dollar depreciating.)

Yep, I googled that
http://news.bbc.co.uk/2/hi/uk_news/2635419.stm

http://www.google.com/search?btnG=1&pws=0&q=bbc+anti-america

First result

http://news.bbc.co.uk/2/hi/uk_news/4881474.stm

Christian Cox, a US citizen living in London, wrote to the BBC news website to express her concern about the amount of abuse she receives because of her nationality.

She says the level of anti-Americanism she has experienced "feels like a kind of racism".

2nd http://www.bbc.co.uk/news/world-south-asia-13001640

Anti-US sentiment is 'rife' in Afghanistan and Pakistan

Quiz: How widespread is anti-Americanism? is the 3rd result

UK Prime Minister Tony Blair is warning of the dangers of anti-Americanism, saying alliances with the US have brought decades of stability, while pressing the US to accept the importance of world issues like the Middle East.

The 4th result seems on the face of it to be what you're talking about, entitled 

This article starts with a rant - "While the Western world awaits, with trepidation, the onslaught of Al-Jazeera International, another channel has been making increasingly disturbing inroads into the U.S. ", then continues with some more ranting

Furthermore, “BBC executives admitted the corporation is dominated by homosexuals and people from ethnic minorities,” said Simon Walters of the Mail (a competitor of the BBC), and “deliberately promotes multiculturalism, is anti-American, anti-countryside and more sensitive to the feelings of Muslims than Christians.”

and then ends with a bit moer ranting.

So I have googled this, now, what you will do is apologise to the BBC. It doesn't HAVE to be in an email to them, it will still be meaningful if it's just an apology on VGChartz

I think as many others have pointed out the decline of the US is focused on it's economic and political clout not military. Also I think your analysis of the Iraq and Afghan situation is just far too basic. There's a complex web of reasons why Iraq and Afghanistan might turn out to be a strategic failure (I say might cause there is still the possibility the Pentagon will get it's permanent military base in Iraq that it so desires).

Thing you have to remember is as a share of world trade the US has been in decline since pretty much post WWII after European and Japan centred economies started to take off. It went from 50% at the end of WWII to less than 25% today though it is far richer today then it was when it had half the words trade so it's no bad thing from a US point of view. The main difference now is it has to compete with very fast growing economies of countries who are very independent of the US. At least with Japan and Europe they were junior allies and still under the influence of the US so America had some leeway with those countries but with China and India and other members of BRICS it doesn't really have much say in how they run their internal affairs. South America has finally after 500 odd years of domination started to develop it's own independent path and we are seeing a wave of democratic uprisings in the Middle East that have either overthrown despotic rulers allied to the US or severely challenging those that are clinging to power. So economically and politically there is an evident decline.

Militarily the US is stretched no doubt about it and it's costing them a fortune. Though it's by far the most powerful nation on earth, it can't pressure everyone since some countries have nukes while others (inc those with nukes) have developed sophisticated asymmetrical tactics to somewhat offset the overwhelming conventional superiority of the US. It's a difficult catch 22 situation for the US since it's stuck between a rock and a hard place. If it draws down it's global military reach it will save an enormous amounts of money however it will also lose it's critical strategic leverage that it currently holds over it's industrial rivals.

However the US has been through severe crisis before and survived and it's competitors such as India and China have massive amounts of poverty which they need to address and huge internal problems of which the US has nothing like. We are talking about massive corruption, sometimes violent ethnic and religious tensions, major insurgencies, terrible environment degradation, lack of freedom and serious human rights issues. Just cause the US is going through a decline now doesn't mean to say it's a permanent one or that it's industrialised competitors won't suffer from economic issues at some point (cough*Japan*cough).

Btw why do you feel the BBC is anti-US? Do you say that because it's not pro US foreign policy enough like say Fox News? I think nowadays the BBC has moved more right after it was attacked for being too left liberal (like a lot the media really to be fair).

The maximum territorial influence of the USSR was in 1960. 1961 was the official Sino-Soviet split. The USSR had Eastern Europe and (disastrously) Afghanistan. Cuba and Vietnam stationed some elements of the Soviet military. And that's it. Now compare that with US influence during the Cold War. Always far more substantial, far more wealthy and with far more powerful allies.