Here's a little poem, by an American poet, about what the world would be like without AmericaQUOTE(from the poem)
..Sometime when you feel that your going
Would leave an unfillable hole,
Just follow these simple instructions
And see how they humble your soul;
Take a bucket and fill it with water,
Put your hand in it up to the wrist,
Pull it out and the hole that's remaining
Is a measure of how you will be missed.
You can splash all you wish when you enter,
You may stir up the water galore,
But stop and you'll find that in no time
It looks quite the same as before.
The moral of this quaint example
Is do just the best that you can,
Be proud of yourself but remember,
There's no indispensable man.
The world would undoubtedly be different if America had never existed (which seems to be the premise of the debate questions, as opposed to "America had existed and had progressed and contributed exactly as per the historical record, but suddenly dissappeared at some past point").
However, precisely
how different is open to question. After all, the thinkers who inspired the ideal of America were prt of the European (specifically, the Scottish) Enlightenment of the 17th and 18th Centuries.
Without an American Revolution to inspire it, it is possible that the French Revolution would never have taken place. However, it is also
possible that it would have taken place exactly as it did, or as it did, but a few years sooner or later.
It is also possible that, with nowhere safe to emigrate to, most of the British and other European victims of religious and cultural persecution who founded, developed and extended "America" the concept would have stayed where they were. It is therefore possible that the American Revlution, in substance at least, might have taken place in Britain itself, leading to a British Republican form of government. (how I wish his were the case!).
As for speculations about the outcome of the Second World War, if America didn't exist at all, then
moif has it right - there probably would not have
been a second world war. For this reason - the First World War would not have been clearly won or lost by either side. Instead of clear victory for the Allies over the German and Ottoman Empires, it would likely have petered out into stalemate. Germany would not have been forcibly emasculated, leaving no resentful population open to the siren song of someone like Hitler, and Britain and France would not have been in a position to carve up the former Ottoman terriories in the Middle East. The House of Saud would never have come to power, so while extremist Islam might well have arisen, it is unlikely that it would have attracted significant funding or popular support, since the Caliphate would have staggered onwards in the model of a Western monarchy, as it had done for the latter part of its existence.
Without a Hitler, Fascism would not have gained a widespread foothold and almost certainly not gained power, instead operating as a simply political movement as it has in parts of Europe all along. So there would have been no Holocaust, and no large-scale movement of Jews into Palestine, and no British mandate over the lands to hand over to them, either. In turn, there'd be no Arab-Israli conflict. There would likely be Muslim-Jewish conflict in the area, but probably in the form of Jewish Zionist terrorism against the Ottoman or post-Ottoman governments.
Also, with strong German and Austro-Hungarian Empires still in place, the Westward spread of Soviet influence may not have been possible, so there may not have been any need for a Berlin airlift or a Cuban missle crisis.
On a more positive, pro-USA note, I think
moif is also right to suggest that, without a temperate part of North America to exploit (Canada is, let's face it, a bit too cold to be worth a three-month ocean crossing for late medieval explorers and their followers), the competition between European powers for wealth and resources would have focused on South America instead.
Given the relative strengths of those Empires over the time of Imperial expansion, it's entirely possible that Britain may have gained the upper hand, and that within 100 or so years, English settlers would have taken ideas from the Scottish Enlightenment, mixed in their own ideas on what government should and should not be about, and fought a war against British colonial power to establish their own democratic Republican government based on ideas of creator-endowed, self-evident liberties. (Critically, enabled by French military power.)
So we might all now be having this conversation about what would happen if the United States of America didn't exist, and the rest of the world might be exactly the same. But the national bird of the USA would be a scarlet macaw or an Andean condor instead of a bald eagle, and the Golden State, just beyond the Rockies, would be in what is now Peru, and Mark Twain would have written about a boy having adventures on the steamships and shores of the river Amazon or Plate.
Mexican immigration might still be a problem, but for the Northern border states, not the Southern ones.
Heck, there might even have been a North vs South civil war, won by the Federalist South against the States'-Rights North, with a historically useful abolition of slavery thrown in (South American plantations used slaves just as much as the North, which is why there are now so many black people in Brazil, though they have had much more racial mixing than North Americans, so we don't even have to imagine that too much, and there would likely have been little impact on British or Portuguese dominance).
Without America, then, it's true that many of the doom-and-gloom scenarios could have been in place, but some of the good things America and Americans have done would have been done by someone else. Also, many historical mistakes and missed opportunities would have been avoided (or taken advantage of).
Human nature being what it is, I find it quite unlikely that, all of us having grown up in this notional "world without America", would know or feel any differently then we do now. To coin a Rumsfeldism, we don't know what we don't know, so our parallel, non-USA world might (would) be different, and might be better or worse, but we'd have no sense whatsoever what those differences and (dis)advantages were.
It's as daft as me saying "what would the world be like without Britain?". Chances are it would be much the same in most respects, except we'd now be typing in French or Spanish and not English (it probably would NOT be German, Russian or Japanese).