What Makes A Penny Rare?

Which penny are you talking about?

Is it about a cent (US, Canadian, Australian, etc.)that many nickname "penny", or British (Empire / Commonwealth) one? Decimal, predecimal? Which era? Milled, hammered?
Too many parameters of freedom. You need to be more specific to get a competent answer.

LOL what makes any coin Rare? When one peruses ebay every second coin appears to be described as rare. Take a new Zealand coin for example....the 1935 3 pence. It a coin that NZ collectors will hunt for and is regarded as a key coin and the majority of collectors would describe it as rare . In 2004 I was horrified when speaking( in person) to a NZ dealer, that dealer stated in his opinion that particular coin was as "common as muck" I recall words to the effect that if you want one and are prepared to pay you will find one in a week. I never forgot that statement and realized later how accurate it was. Although it is regarded as rare ( mintage aprox 55000) it is reasonably obtainable. In comparison other NZ coins are made of unobtainium; such as the 2000 fantasy $50.00 coin from the Chatham islands. { It was an issue that breached NZ monetary law and the dies and nearly all existent coins were seized approximately 10-20 coins remain in private hands..}Try finding one I suspect you will have to hunt for several years to find one. Rare also doesn't mean expensive....I have a counter-marked Austrian 25 Schillings...as one of a maximum of 5 its rare but I doubt anyone would pay me more than US$30.00 for it.