And so they meet again at Euro 2012.
This time, however, Spain and Italy are playing for the European Championship and a place in the history books.
The Mediterranean rivals meet Sunday in Kiev's Olympic Stadium, three weeks after they drew 1-1 in their opening match of the tournament's group stage.
As the defending champion and World Cup holder, Spain is bidding to win a third straight major title, cementing its place as one of the greatest national teams. It would also match Germany's record of three European Championship titles.
Only the unpredictable Mario Balotelli and a surprising Italy team — orchestrated by Andrea Pirlo — stand between Spain and what many see as its destiny.
Even Italy coach Cesare Prandelli reckons that Spain is the best bet to lift the trophy.
"At the moment, even if I open my eyes, I am still dreaming," Prandelli said after his side's 2-1 victory over Germany in the semifinals, when Balotelli scored both goals.
"Spain remain favorites because of the years of hard work that they have put in. They have been dominant in every game they've played so far."
Spain hasn't lost in a European Championship since 2004 and has already matched West Germany as the only defending champion to return to the final after winning the World Cup. The West Germans managed it in 1976, but subsequently lost to Czechoslovakia following Antonin Panenka's famous chip shot in a penalty shootout.
This final brings together teams with players brazen enough to have successfully copied Panenka's audacious spot kick during their penalty shootouts in the knockout rounds. Spain defender Sergio Ramos used it in the semifinal win over Portugal, after Pirlo employed it against England in the quarterfinals.
It also features the tournament's best defensive team against one of its most exciting attacking squads.
Spain has not conceded a goal since that opening draw with Italy and hasn't been scored upon in nine elimination games at major tournaments. Balotelli, Antonio Cassano and Pirlo are leading one of Italy's top attacking teams in recent history.
"We always just tried to play, I think that is our strength," said Prandelli, whose team is bidding to give Italy its second European title, the same number as Spain and France.
"When we started off at this tournament, we were convinced that by working in a certain way we could become a proper team — not just a quality team, but also a team with the right spirit."
Though Balotelli's selection had been in doubt due to troubles both on and off the pitch at Manchester City, the 21-year-old Italian of Ghanaian descent has scored three times at Euro 2012.
"I waited a long time for this moment, especially because my mother came all the way here and I wanted to make her happy," he said after the victory over Germany.
"This is the greatest evening of my life, but I hope Sunday will be even better," added the striker, who has a chance to finish as the tournament's top scorer with one more goal.
"For the final my father is coming, too," he added. "So I hope to score . . ."
Along with their players, the Azzurri also have an encouraging statistic on their side: Spain hasn't beaten Italy in a competitive match that didn't end in penalties since 1920.
Spain's attack has featured a rotating cast of forwards, with attacking midfielder Cesc Fabregas usually being preferred to striker Fernando Torres. On Sunday, coach Vicente del Bosque is likely to repeat the 4-6 formation he first deployed against Italy on June 10.
Substitutes Pedro Rodriguez and Jesus Navas have had impressive tournaments, and Del Bosque certainly values the contribution of players who don't feel slighted by being on the bench.
"When you send out a substitute who is upset it always makes things more difficult. When you send out a player who is happy and ready to play one minute if that's what's needed, that is very important," said Del Bosque, who can match West Germany's Helmut Schoen as the only coaches to have won a European Championship and a World Cup.
Del Bosque admitted that Portugal not only made Spain look sloppy for over an hour, but had taken his players "to the limit."
However, his team's extra day of rest compared to the Azzurri will help with preparations, while Italy is keeping an eye on any injury problems after Balotelli came off in the second half against Germany due to cramps.
"We're proud of what we are doing and, of course, we hope to achieve what no one else has done before," Del Bosque said, before touching on what victory would mean with an economic crisis back home.
"It would be good for everyone, for Spanish football and for our country."
Paul Logothetis can be reached at: www.twitter.com/PaulLogoAP