Picture : French defender Lilian Thuram was the first to cross 13 games.

Most games: development of the UEFA Euro Record 

In this post, we trace how the record for the number of matches played in the final stages of the European Championships has changed from the beginning to the present day.
Three players of the Soviet Union national team - Valentin Ivanov, Lev Yashin and Viktor Ponedelnik - had played four matches by the end of Euro 1964 (the maximum possible by that time). n the next edition, their compatriot Albert Shesternev joined them, and in 1972 several more players did it. 
It got to the point that at Euro 1976 already 9 people together held a record with the same modest figure of 4 matches, until finally the Yugoslav Dragan Džajić played his fifth match (picture down).

The time passed, and the next stumbling block was the number 13. Following Jürgen Klinsmann's first reaching this milestone in 1996, by 2004 again 9 players gathered at this mark. Lilian Thuram was the first to cross it then.
At the moment, Cristiano Ronaldo holds this record, moving it from 16 to 21 matches. We expect from him a further leap upward at Euro 2020.

Valentin IvanovSoviet Union421/06/1964
Viktor PonedelnikSoviet Union421/06/1964
Lev YashinSoviet Union421/06/1964
Albert ShesternevSoviet Union408/06/1968
Flórián Albert Hungary417/06/1972
Anatoly BanishevskySoviet Union418/06/1972
Yury IstominSoviet Union418/06/1972
Vladimir KaplichnySoviet Union418/06/1972
Dragan DžajićYugoslavia417/06/1976
Dino ZoffItaly515/06/1980
Hans-Peter BriegelGermany720/06/1984
Karlheinz FörsterGermany720/06/1984
Karl-Heinz RummeniggeGermany720/06/1984
Harald SchumacherGermany720/06/1984
Uli StielikeGermany720/06/1984
Rafael GordilloSpain724/06/1984
Luis ArconadaSpain724/06/1984
Rafael GordilloSpain811/06/1988
Andreas BrehmeGermany1018/06/1992
Jürgen KlinsmannGermany1223/06/1996
Thomas HäßlerGermany1320/06/2000
Peter SchmeichelDenmark1321/06/2000
Dennis BergkampNetherlands1329/06/2000
Laurent BlancFrance1302/07/2000
Didier DeschampsFrance1302/07/2000
Paolo MaldiniItaly1302/07/2000
Lilian ThuramFrance1321/06/2004
Zinédine ZidaneFrance1321/06/2004
Lilian ThuramFrance1425/06/2004
Zinédine ZidaneFrance1425/06/2004
Karel PoborskýCzech Republic1401/07/2004
Luís FigoPortugal1404/07/2004
Lilian ThuramFrance1613/06/2008
Edwin van der SarNetherlands1621/06/2008
Cristiano RonaldoPortugal1618/06/2016