Ukraine (fourth ranked third placed team, from Group C)
England (Group D winners)
Czech Republic (second ranked third placed team, from Group D)
Denmark (Group B runners up)
The group winners who didn't make it through the round of 16 are Netherlands (Group C winners), Sweden (Group E winners) and France (Group F winners).
Despite being the "group of death", with France (currently ranked second in the FIFA World Rankings), Portugal (currently ranked fifth in the FIFA World Rankings), and Germany (currently ranked twelfth), all of whom made it through to the round of 16 (Germany as runners up and Portugal and the first ranked third place team), plus Hungary, no team from Group F made it through to the quarterfinals.
I have a hypothesis - across highly competitive international tournaments played over a month or so, like the World Cup or the Euros, teams that get through from a "group of death" hardly ever go on to win the tournament if at all.
It's almost like getting out of the group takes its toll, and in highly competitive tournaments, where the smallest margins can make all the difference in outcomes, the toll is enough to prevent the teams from going on to win the tournament.
Someone should do a detailed analysis. I'm not sufficiently interested in international football to do it myself.