Hosts Portugal, Italy, the 2000 runners-up, the Czech Republic, England, Germany, the Netherlands and Spain, are also realistic contenders to win the Henri Delaunay Trophy.
But France remain the team to beat, favourites to become the first side in the championship's 44-year history to retain the title.
The French are unbeaten in 18 matches and have not conceded a goal in almost a year, by far the best recent record of the 16 finalists.
Determined to succeed with style after their abject failure in the 2002 World Cup, France revealed a not-always obvious tenacious side when they beat Ukraine 1-0 with an 88th-minute Zinedine Zidane goal in their final warm-up game.
Their next opponents are England in Lisbon on Sunday, one of the most eagerly awaited clashes of the tournament.
With so many France players facing their English club team mates, the match will have the intensity of the fiercest derby, and England, buoyed by their 6-1 win over Iceland, will be equally determined to start with a victory.
England, however, not only have the opposition to worry about but also their own fans.
UEFA has threatened England with immediate expulsion if there is any repeat of the hooliganism that blighted Euro 2000 and England coach Sven-Goran Eriksson has pleaded with his team's fans to behave.
Croatia, who beat Denmark 2-1 in their final warm-up, and Switzerland, who scrambled a 1-0 win over tiny Liechtenstein in theirs, complete the group.
PORTUGAL READY
Portugal's opening match against Greece in Porto on Saturday heralds the start of the biggest sporting event staged in the country and completes a remarkable achievement for the host nation.
Portugal saw off a challenge from neighbours Spain to win the right to host the tournament and, after causing UEFA initial fears over stadium-building plans, the Portuguese have worked wonders.
All 10 stadiums in the eight venue cities have either been built as new or refurbished and the tournament has captured the imagination of this small, soccer-crazy
Portugal are bidding to become the first hosts to win the European Championship since France in 1984 in a tournament that represents the last chance for the surviving members of their "Golden Generation" to win a major honour.
Luis Figo, Rui Costa and Fernando Couto were all members of the teams that won the 1989 and 1991 World Youth Cups and will be more eager than most to emerge victorious.
While England face a derby against France, Portugal face one against Spain who they meet in their final Group A match in Lisbon.
With Russia and Greece making up that quartet, much is likely to depend on the Portugal-Spain match. If Groups A and B go according to form, Spain or Portugal should meet England or France in the quarter-finals.
ITALY INTENT
Italy head for Portugal, intent on going one better than four years ago when they let the title slip in the dying minutes of the final.
With Italy leading 1-0, Sylvain Wiltord equalised for France and David Trezeguet scored a spectacular Golden Goal winner.
Italy beat Tunisia 4-0 in their final warm-up and secured a 2-1 win over Portugal in a friendly in March. Coach Giovanni Trapattoni's team have a resolute look and should qualify as Group C winners before meeting Germany, the Netherlands or the Czech Republic in the quarter-finals.
Those three former winners make up Group D along with outsiders and newcomers Latvia and all travel to Portugal in vastly different frames of mind.
Germany, who can never be under-estimated in any tournament, have had a poor build-up, losing 5-1 to Romania in April and 2-0 to Hungary on Sunday alongside a 2-0 win over Switzerland and a 7-0 romp over Malta.
The Czechs have lost a little lustre after their 20-match run ended in March but have an excellent record in this championship, winning it in 1976 as Czechoslovakia and finishing runners-up in 1996.
The Dutch, as ever, are talented but whether they have the mental resolve and team harmony to repeat their 1988 success remains doubtful. Latvia are just happy to be involved, and showed against Turkey in the qualifiers, that they should not be under-estimated.