I'm young and also didn't become a serious viewer or fan until 2012, so I'll go through Euros 2012 and 2016 + WC 2014.
The performances I truly remember from Euro2012 are Jordi Alba and Mesut Ozil (until the semis, in which he was godawful). Iniesta won the Golden Ball, but Alba was the player on that Spanish squad who really impressed me, mainly because I already knew that Xaviesta were world class, whereas Alba was more unknown to me.
Robben in 2014 played some of the best football I've ever seen, he was absolutely lights out. He had a really bad Euro2012 (as did the rest of the Dutch squad), so I was blown away by how dominant he was in Brazil. The other guy who I don't think gets enough credit when people talk about that WC (conversations generally, justifiably, focus on James, Messi, Muller, Robben, etc.) is Mats Hummels. He and Boateng were dominant in that tournament.
Euro2016 was just all Griezmann all the time. I know lots of people here were still skeptical at that time about how high of a level he could hit (
@Evilo specifically, I do recall), and holy mother of god was he good.