1. The 741 obviously, although the 301A is practically the same part and more universal. There is little reason to use a 741, but the 301A has all of the same virtues and additional capabilities beyond most modern parts through its external compensation which allows clamping.
2. The TL071/TL072/TL074 are the last survivors of the jelly bean JFET input parts. The National LF series JFETs were jelly bean parts in the past.
3. The NE5532, or one of this variations.
4. The OP-07 despite being completely obsoleted by improved parts. The virtue of the OP-07 is that it is widely second sourced making it the cheapest precision part.
5. LM358/LM324 - These are dual and quad versions of the same part. The single version never became popular.
The RC4558 is sometimes called equavalent to 741, but it is actually a quite differente OP: higher BW, lower noise,... more like half the way to the NE5532. Closer to an dual 741 is the MC1458 /1558. The RC4558 is still a good yellybeen part - wish there would be a single version (because of the lower power).
The RC4558, like the RC4136, use a completely different topology than the 741. The 741 and 301 use cascaded NPN and PNP pairs to combine the performance of the NPN transistors with the high base-emitter breakdown voltage of the PNP transistors. The RC4558 and RC4136 use only the PNP differential pair. Besides the performance difference, the input bias current is reversed between the 741 and 4558. I am not sure if the RC4558 and RC4136 achieve small die size through transconductance reduction; the schematics do not show it but often it is left out, and the shown compensation capacitance is pretty high, although that could be marked wrong also.
The 1458 is closer to a dual 741 because it uses the same NPN and PNP input stage arrangement, but the 1458 includes transconductance reduction so the internal compensation capacitor can be much smaller saving space and allowing room for a dual part. The LM348 quad 741 also uses transconductance reduction for the same reason.
AFAIK there is no direct dual or even quad OP07. With the relatively high power consumption this would also no be practical. There are duals and quads from later improved versions - e.g. as my new favorite replacement OPA202 / OPA2202 / OPA4202. In the old days this was more like AD704,705/706.
The OP-207 was a dual OP-07. If PMI made a quad OP-07, it should be in their last databook before Analog Devices bought them. I doubt a quad OP-07 was ever considered because how would offset null be brought out? The dual OP-207 was only available in a 14 pin package, and they even brought out separate power supply pins. It was probably a single die and not two OP-07 dies because of parameter matching.
Linear Technology made a dual OP-07 in the form of their LT1002 which was functionally and pin compatible with the OP-207, so PMI was not the only one who saw a demand for such a part.
How did these end up being made by multiple manufacturers under the same model name? Does the mask mark expire and somehow another company either gets ahold of it or reverse engineers it from samples?
Reverse engineering was common, and then patents were either cross licensed or sometimes an implementation was made which avoided the patents. Sometimes even the same part from the same manufacturer is implemented later with a different layout.
Also how does it make economic sense to use masks from the 70s?? For maximum cheap, you should balance cheapest process technology with maximum parts per wafer and minimum out-of-tolerance yield loss.
These parts still require a 44 volt bipolar NPN process with lateral PNPs for level shifting and high base-emitter breakdown voltage, which means using the processing steps of an old process if the performance and functionality is to be comparable, and those old processes use a minimum number of mask steps making them less expensive.
How much smaller is a "modern" 44 volt process compared to that? Parts like the 1458 and 348 were made much smaller on the same old process allowing dual and quads by using techniques like transconductance reduction.
As far as I know, a modern 44 volt NPN process can be implemented with finer geometry, and I am sure this has been done for "modern" 44 volt precision parts, but that would have little benefit in area reduction of a 741 design with its large internal compensation capacitance.
But each of these parts has a separate lineage of improved versions from each manufacturer. Those derivatives are unsurprisingly rarely made by more than one manufacturer. Surprisingly though, such parts rarely compete with the ancient originals on cost and somehow never manage to obsolete them. Was copying one another's model names just a trendy thing that went away by the 2000s?
Those improved versions take just as much area to provide the same features so are not any cheaper. When I look through TI's parts, the only 741 replacements which are less expensive are parts which use less die area because of a smaller compensation capacitor allowed by transconductance reduction. The smaller "improved" 741 is the 1458.
Note that one of the rare features of the 741 which is commonly not found in modern parts is wide differential input voltage range. This is difficult to duplicate on a "modern" high performance process, and parts built on a modern process with a differential input voltage range greater then about 7 volts are rare or non-existent. Offhand I cannot name any, and I have looked for them before.