If the US stayed out of other countries politics and there were no coups or installation of people favorable to the US what would the world look like?

Most likely some other country (or countries) would simply fulfill the same role of projecting their military and economic power onto the rest of the world to maintain their hegemony. We see this in limited ways already with many other countries, though with a few exceptions, they’re careful in how much they conflict with US interests. One of these, likely China, would move into that role and while the details would be different in some ways, many of the overall dynamics would be similar.

Bananas would cost more

History doesn't provide answers to hypotheticals

The world would be far more Socialized.

Most countries would be socialist.

Well the troubles would have continued. So there that.

The US projects its own interests worldwide but those often overlap with the interests of other as well.

For example, the US often stipulates intellectual property and worker rights in it's trade deals. The US actively protects shipping lanes. The US actively negotiates visa-free entry for American passport holders to other countries. The US invests in the economies of foreign countries to stimulate trade opportunities. The US controls the SWIFT banking network which makes it so that we don't need to send gold bullion or pallets of cash to buy things from other countries, and participating in the system requires member countries to have certain controls in place that attempt to block bad actors. The US, through it's embassies and ambassadors, deploys it ideology to foreign governments, and makes deals that allow foreigners to invest in the USA and Americans to open businesses in foreign countries.

The US actively shuns and makes life difficult for menace dictatorships on the global stage by creating trade exclusions.

There have been coups since the beginning of time and always will be, as it's human nature. Many citizens of other countries have no belief that the future of their country belongs to them after decades or centuries of dictatorships or kingdoms. On the whole, history shows that kingdoms rise and fall for many reasons and the people sometimes benefit and sometimes suffer for it.

Obviously it's a highly complex topic, but if the US wasn't doing these things, then Russia or China would be, or there would be more powerful regional factions, which could reduce the size of the world in terms of travel and trade options for many.

Whether the US is the right one to be in control of this at this point in history is a matter of intense debate among some, but it could absolutely be worse than it is now.

Difficult to say. For starters, we can't know with certainty the full list of countries that were affected. We don't know all the ways countries were affected. There's so much we don't know that it's really impossible to say.

On a tangentially related note, this documentary series from BBC4 is a fascinating insight into the decision making process the US went through over dealing with foreign mass atrocities over the past 40 years: Iraq, Bosnia, Rwanda, Syria etc.

Warning: they do not hold back with the imagery of these events.

Corridors of Power: Should America Police the World?

Definitely a better place.

Other countries would probably still have some similar shit. People are people.

It really depends on how far back you want to look.

If the US was to suddenly stop projecting its interests internationally, then as others have mentioned, then likely the world work become somewhat more socialized. European countries would probably step up and try to keep China in check, but without the US contributing to these efforts, it would cause a significant strain on their military resources.

If the US was to take an isolationist policy 100 years ago, then there is a good chance that WW2 would have been won by the Axis. The Allied forces likely would have put up a good fight, but I'm not sure they would have emerged victorious against the combined Axis forces. The war in the Pacific would have raged on much longer, and without nuclear weapons, there would have been an extreme loss of life invading Japan. At the very least, WW2 would have lasted much much longer than it did. Depending on the outcome, plenty of countries might currently be speaking German and debating if they should tear down 80-year-old statues of Hitler.

Germany would have taken over Europe.

The "It's a Small World" ride at Disneyland.

The issue comes down to imperialism imo.

Western societies have an imperialist belief that we should be at the head of the table when it comes to the world order, politics, and having a say about what happens outside of our borders.

This is ingrained in all of us from a very young age by design. They've been doing it for millennia, and it's been working pretty well, so no need to change tactics.

It's also why non-western nation-states aren't as involved directly in the politics of other nations. It's not really a part of their ethos as a culture.

Japan would probably still be isolated.

in 1853 US sent warships to force Japan to trade with the west.

Its imperial aspirations were fueled by western thought.