When the Euro was officially introduced as a valid currency back in 2002, I started collecting the different Euro coins according to year, country, and mint. I bought folders from “Leuchtturm”, where the coins are put into. These folders are worth several hundreds of Euros, even if they are empty. But yet, I own about 1,200 Euro in different Coins in my collection. I was lucky to find some exchange partners. Some of them really had amazing coins.
The rarest coin I own is a “regular” 2 Euro from France, from 2009. If you had one in your hand, you would probably not recognize it as rare, as long as you aren’t a collector for yourself.