Ugh. Wish I'd seen this thread sooner, there's a lot of misinformation and confusion here.

What you're asking about is actually called the legal age of majority - which is the age at which someone is considered a legal adult. As others have pointed out, various "adult" responsibilities sometimes come sooner or later than that. You can drive long before you reach the age of majority in most places, for example, and in the US you reach the age of majority (18) before you can legally drink (at 21). But for most (legal) purposes, the age of majority is the point where you're treated as an adult and are no longer considered a child.

The US, UK, and Canada all used the common law age of majority of 21 up until the middle of the twentieth century - the UK lowered its age of majority from 21 to 18 in the late 60s, and most Canadian provinces & US states followed piecemeal over the next 10 years or so.

As for why 18 is considered a "standard" age of majority these days, that's tough to answer, but the most likely explanations are that 18 has often been the minimum age for military service (the argument that young soldiers should be treated as adults was one of the primary reasons for lowering the age of majority), and that this is about the age where most people have finished school and either go to college or enter the workforce (note, though, that that's only been the case for the last 50-60 years or so). Both of those things create a strong incentive to treat people as adults around 18.

I don't think there's much of a connection to King Tut here though - that's very far removed from the present both in terms of time and cultural difference, and different societies have set a wide range of ages for legal adulthood since then. Even today, setting the age of majority at 18 is far from a universal practice. Basically, the only reason it's widespread now is that enough countries have chosen this age limit to make it a common legal convention, just like the common law age of majority was in earlier years.

this was 3,000 years ago when life expectancy was much shorter and people married in their teens or even pre-teens...

This is a myth. life expectancy [at birth] is a funny thing (as are statistics in general) that does not accurately reflect when people actually died.

Wikipedia's example of removing the bias of infant mortality rate and childhood disease:

Life expectancy increases with age as the individual survives the higher mortality rates associated with childhood. For instance, the table above listed the life expectancy at birth in Medieval Britain at 30. Having survived until the age of 21, a male member of the English aristocracy in this period could expect to live: 1200–1300: to age 64, 1300–1400: to age 45 (due to the impact of the bubonic plague), 1400–1500: to age 69, 1500–1550: to age 71

You can find plenty of other adjusted charts that use various ages of viability through out time to account for child and infant mortality.

The young marriage is also somewhat of a myth, woman might have married younger than today in attempts to maximize child bearing years, but that does not mean having children at the earliest possible age as that its self may complicate a woman's ability to produce more babies later on (remember with such a high infant and child mortality rate that women must have more children to maintain the population level) , but in say Rome Men did not marry until their mid to late twenties.

In your example of free to rule on ones own, that would really be more of a decision made by the regent(s) and the ruler themselves. Who is more powerful and has the will to rule? (totally under dispute as to why but notice Tut did not live too long after he took power for him self...)

18 in no way has been a continual age of "adulthood" and is fairly modern as a standard age of majority. In the US voting rights (which I'm guessing your taking as the modern equivalent of adulthood) were only guaranteed to citizens over the age of 21 until 1971, and according to the constitution no one can become the president of the United States until they are 35 years old (sorry people looking to be a modern King TUT).

Mod note: we've done a bit of a clear-out here. Please do not simply provide counter examples, nor lists of what people are permitted to do at age x in country y. These are anecdotal, meaningless single data points, and don't in any way answer the question.