No, they did not always have launch codes. Additionally, even after the advent of "launch codes" for US nuclear weapons it took quite some time for them to be effectively put into use.

The system is called a Permissive Action Link (PAL). The very first systems were basically just combination locks that were inserted into key components of nuclear bombs (electrical circuits, mechanical mechanisms necessary for detonation, etc.) The technology was soon upgraded to electromechanical locks developed by Sandia labs. In 1962 JFK ordered PALs to be used for all US nuclear weapons deployed in Europe (he did so based on concerns arising from the experience of the Cuban Missile Crisis). This was done but Strategic Air Command (SAC) set the code for them to all zeros (though this is disputed), without informing the president, this code was not changed until the mid 1970s.

The technology for PALs has improved consistently over time (e.g. increasing the code length from 4 digits to 6 and then 12 digits) but almost all of it is shrouded in secrecy. Through the 1970s almost all US nuclear weapons had been locked down, some with modern PALs some with crude locks. It wasn't until the near end of the Cold War in the late '80s for all US nuclear weapons to be outfitted with PALs.

As mentioned, not all nukes have always used "launch code" systems. The earliest US nuclear bombs did not have such codes and were essentially just simple bombs. The US has offered to share information about PAL technology with other nuclear armed states, has done so with at least France and almost did so with Pakistan and China (though in both cases decided against it). Notably the UK's nuclear weapons are known to lack any sort of launch codes. The crew and captain of a British ballistic missile submarine is fully capable of launching its complement of warheads without any outside communication. The Soviets have developed their own version of PALs but little is known about it.

I'm not aware of any other weapons using similarly sophisticated control mechanisms. As for public awareness, at least by the early 1980s the public had become aware of the use of launch codes and that had been integrated into the tropes for nuclear weapons in hollywood at the time. Notably the 1964 movie Dr. Strangelove contained no mention of PALs, as the technology was still classified at the time.

In the popular nomenclature there are several things that get called "launch codes" so we should probably define them here.

There are the "codes" that the President has that confirm his identity as the President. This is what the football/biscuit setup developed in the 1960s was meant to do. These "codes" are really quite simple, just numbers and letters that match what someone at NORAD or the NMCC is going to have in their hand, so they can say, "yes, this person on the other end of the phone, making an order to use a nuclear weapon, is the President, and I authenticate his identity." These are today created and distributed by the NSA, but they are literally on a piece of laminated paper — nothing super high-tech. They are not transmitted to commanders in the field or used to unlock weapons or anything like that. They are just used to make sure that the order (which goes from STRATCOM to be acted upon) is authenticated, i.e., from the President or a designated successor.

There are the Permissive Action Link (PAL) codes which are used on gravity bombs and tactical nuclear weapons. These are complex systems of authentication and unlocking that are built into the weapons themselves at this point. In their earlier versions they were basically large padlocks. These were pioneered in the late 1950s, and put into place largely in the 1960s, first on weapons deployed overseas (NSAM 160, created by JFK, ordered this), and then on ones deployed domestically. The PAL system is meant to make unauthorized use of the weapons impossible. The "codes" in this case are kept by division-level commanders and then distributed to the people in the field after a legitimate (authenticated) employment order is received. In modern PALs, putting in the wrong code or tampering with the PAL device will disable the weapon (ideally permanently). The reason these were developed was that the US was deploying many thousands of weapons overseas, sometimes in situations where there was very little US oversight. So the Jupiter missiles in Turkey are a famous case of this: if the Turks had hit the American officers over the heads with hammers and taken their launch keys, they'd be nuclear powers. PALs were a way to guarantee American authority over the use of the weapons, and to make sure (in later, more sophisticated versions) that if someone stole a weapon they wouldn't be able to use it. To use a PAL, you need a PAL controller system — a separate system outside of the weapon itself that interfaces with the weapon (modern ones attach to a laptop, which attaches to the weapon).

Lastly there are the missile launch codes, which were added to domestic ICBMs somewhat later, at great resistance. These are not PALs and they are just meant to be one extra layer of security against false launch. These are the ones alleged to have by set to all zeroes by the Strategic Air Command in the 1970s. They are one of several switches that are meant to make sure that the weapon is not triggered in an unauthorized or accidental way (there are also "environmental switches" in the weapons that basically mean the weapon won't complete the detonation sequence if, say, it doesn't detect that it's been shot in a missile into space at the right distance, etc.). This is not a big bulky PAL system, it's just a set of numbers you have set while you are going through the launch sequence.

Considerations over authorization and Command and Control issues (which is what this is classified as) evolved over time, since even the Manhattan Project. It would be a long thing to try and write them all out — it long predates the "codes" approaches. In the early post-WWII period, the weapons were not even given to the military, but kept in civilian hands. Under Eisenhower, new weapons designs and strategies meant the dissemination of thousands of weapons to the military, and many thousands overseas as well. This dispersion of totally unsecured weapons — weapons that anyone could use if they physically had control over them — deeply disturbed Congress, the weapons designers, and later the Kennedy administration. (It did not disturb the military, who generally resisted anything that might make it hard for them to use the weapons when they thought it was appropriate.) It took many years and many fights to make the weapons more secure and harder to use.

Public knowledge of the "football" started around the 1967, but wasn't really outlined much more until the 1980s. See this nice article and collection of documents from the National Security Archive. I don't have a sense of when PALs became well-known but I would bet it was not until the 1980s. But I'll find some time (not today) to look into that. The allegations about the missile launch codes did not come out until the 1990s. In general the understanding of how these things worked became much more well-known in the early 1980s, and more attention started to get paid to Command and Control issues at that time.

For further reading, Schlosser's Command and Control is good, Bruce Blair has written a lot about these issues, and if you have some time to kill, Sandia National Laboratorie's Always/Never: The Quest for Safety, Control, and Survivability is a pretty good documentary on the political and technical efforts that went into assuring the safety and surety of the weapons in the USA.

At one time all information concerning "launch codes", "nuclear release" and "PAL" devices was Top Secret and "the presence of nuclear weapons will neither be denied or confirmed". How much of that information has been declassified is unknown to me. Just because Top Secret information is printed in the NYTimes or "everybody knows that" does not declassify the information. All nuclear weapon information, release, use and everything was controlled by the Joint Chiefs of Staff. Not Dept of Defense but JCS.

To my knowledge, the use of nuclear weapons has always required presidential release. The wrinkle was how the weapons were armed or if armed all the time. Just because the weapon was not authorized didn't mean a commander couldn't shoot it. Consider General MacArthur's desire to use nuclear weapons during the Korean War but couldn't/wouldn't cause Truman would not okay the shoot. From that evolved a secure and very Top Secret process to arm the weapons.

I would suggest "launch codes" would be an incorrect term, at least in some situations. "Release Code" is more accurate. The "released code" activates the PAL. The "PAL" device allows the nuclear warhead to be armed, not necessarily to launch. Once activated the operational situation might not require immediate launch, especially when the "special weapon" is a tactical nuke as opposed to an ICBM.

Consider a build up of hostility between the US and Russia. The president might release the weapons to be armed and ready, but not to launch. It takes time to decode, verify then activate the PAL and arm the weapon.

Many missiles armed with a nuclear warhead may able to launch but will not achieve a nuclear burst, just an HE at best, unless the PAL device is active. Without the secure process to activate the PAL an out of control unit can't start WW3.

The on-site commander would "push the button", this will probably be a lieutenant or a captain. (Yes, a 22 year old lieutenant can launch a nuclear weapon. Sleep well my friend!) To "arm the warheads" generally authorizes the use of the weapon based on "Rules of Engagement". Even a ground pounding infantry private has "rules of engagement". "Rules of Engagement" are more complex than just pushing a button. An officer in the US military takes this stuff very seriously!

The idea only the president could authorize the use of nuclear weapons (arm the warheads) was and is still promoted. This is true but not accurate. It seems most citizens do not know the president can delegate this authority to field commanders. At one time and probably continues, CINCPAC had the authority to "release nuclear weapons". I would guess NORAD commander has authority to arm and launch. Mr. Trump's admiration for the military is such, I would assume he delegates the authority to a theater commander.

The average citizen is blissful in their ignorance. Consider this, the US system is significantly more secure than the Russian.

You might find this interesting: At one time, the US Army placed nuclear warheads on many or most Nike Hercules Air Defense missile systems and these units were located on the US mainland, such as West/East coast and Miami. Nike Hercules has been retired and replaced by the Patriot.