Okay. The coin I (finally) post in this thread won't be anything like the incredible examples I would've posted for 1966 (and that I might yet post for 1945, 1923, and a few other years).
Instead, I chose it because of a funny bit of backstory.
Way way back in my childhood, I already tried to collect coins, but wasn't yet aware that one can actually
buy them; so my collection was essentially limited to what I could find at our home, what I could find at friends' homes, and what I got in change while visiting foreign countries (usually Israel).
Fortunately, with the multiple reforms of the 1990s, almost every home I went to had huge amounts of obsolete currency for me to look through; the most interesting being Soviet coinage (which had so many different dates, and a few denominations that seemed a bit funny[1]).
However, this bunch of reforms making money quickly obsolete meant that most coins I ever saw in circulation didn't have much time to, well, circulate, so were in pretty high grade - what you Americans might call VF. Meanwhile, the Soviet coins had mainly been pulled from circulation in 1991, so they could've circulated - and worn away - for as much as 30 years[2]... a concept that was entirely alien for circa-2003 me.
Let's go for a bit of a history lesson. When the Soviet monetary system was reformed (again) in 1961, coins below 10 kopek were still legal tender in their old versions, but those of 10 kopek and higher had to be made in huge quantities to satisfy the circulation demand. So there was a lot of coins dated 1961 (and slightly less, but still a lot, dated 1962); and they were still common in 1991. Of course, over these 30 years most of them became very worn (much more worn than any coin that didn't have that many years of circulation).
Anyway, returning to me. I noticed that some of the 1961 and 1962 coins lacked some details that were visible on the later examples; in particular, the rim was usually faint or missing. Of course, these details were simply worn away by 30 years of circulation; but, I repeat, to my circa-2003 mind the very concept was alien. So I developed what was probably the simplest theory not involving it: that, for whatever reasons, these coins were minted that way.
Looking at it from a modern perspective, I was ridiculously naive. But I seriously believed that theory; and while I, of course, don't believe it now, whenever I encounter an 1961 Soviet coin with a worn-down rim, I can't help but think of that little theory... if maybe possibly only because it was so funny.
...This particular coin was from the very same bunch I mention below in note 2; so I doubt I could've actually encountered it way back then. It is also rather ugly (the awful photos didn't help - it's slightly less uglier in hand - but it's still not particularly pretty). Unfortunately, I've long since lost most of the coins that could've originally inspired that theory; this one is just an example of how they could've looked



[1] While coins denominated 3 are relatively common, even in decimal currencies, I can't think of many countries other than the USSR and its predecessors that made coins denominated 15

[2] Theoretically, even more; a bunch of Soviet coins I got from one of my non-collecting relatives included a coin dated 1926 - I've lost it since, unfortunately - and for all I know it probably was found in circulation sometime in the 1980s. In practice, excepting a particular single lucky find - which probably deserves its own entry when we get to that date - I hadn't encountered any pre-1961 Soviet coins until much later.