Dfyjkt

Is there a one visa or any paper that lets you enter (almost) any country in the world? For example, you are trusted and record-free citizen of couple countries and you sign something that makes you allowed to enter (almost) any country.

There is no such visa. Every country has its own entry requirements, which will depend on your citizenship, purpose of your visit, and other criteria. While there are some supranatural agreements (Schengen being the most significant) that grant visa holders access to more than one country, every nation considers its ability to admit and refuse foreigners as an element of its national sovereignty and would be highly unlikely to sign on to some kind of global visa scheme like this.

Now, it is the case that some passports grant more visa-free access than others. Various groups attempt to rank passports based on this, you can see one such ranking at The Passport Index. You'll see that German and Swedish passport holders have visa-free access to much of the world, with many European nations, the US, Canada, Singapore, Japan, Australia, and New Zealand enjoying similar levels of access. As you go down the list, more countries require visas in advance.

However, there are still caveats to such access. Even a mighty German passport-holder still needs to complete the online ETA process to visit Australia. People found ineligible through that process will generally need to obtain a visa to be allowed in. You can argue semantics all day (and diplomats do) about whether Australia's ETA, the US's ESTA, Canada's eTA, etc... are really visas or not, but at the end of the day, they are hoops a traveler has to jump through before they're allowed to travel to a country. Other countries issue a "visa-on-arrival," which can be as simple as a counter where you pay a fee to get a stamp.

Also note that, even with a visa, pretty much every country reserves the right to refuse entry at the border. Visas are also granted for particular purposes and durations of stay. Even though I, as an American, don't need a visa to visit the UK as a tourist, I would need one to get a job there or enroll in a university. In addition, the waiver of a visa requirement doesn't normally waive the need to comply with other parts of immigration law, so you could still be refused on the basis of a criminal record, lack of funds, failure to demonstrate an intent to leave, etc... even though you don't need a visa.

In short, immigration law differs significantly from country to country, and there's no reason any nation would sign onto a universal visa like this. Even if such a thing existed, any country could still refuse you entry based on its own laws.

I'll bite. A UN passport (indeed, not a visa, but still only one document).