Greece was a total shock winning the Euro's but so was Denmark when they did it, lots get made out of having world class players but I think when it comes to the Euro's a good team spirit can take you far and choosing the right tactics. Suppose it is easier when it came to Greece as it is like a newly promoted team in the premiership, that other teams don't take serious
Both the Greeks and the Danes won Euro by playing the bread-and-butter of Tournament football: Defend like crazy and counter attack. Once you're out of the group stages, there is no incentive to push forward. If your best asset is your defense (Schmeichel for the Danes, Zagorakis for the Greeks), then use it. Since the game can't end in a draw, the worst case scenario is you take it to penalties.
The US beat Spain in the Confederations Cup by sitting back and waiting for Spain's full backs to come up. Once that happened, Donovan and Dempsey released. The Germans slaughtered teams 3-0 and higher in South Africa by having the best counter-attack in the tournament. The Italians used to win tournaments without scoring more than 1 goal in a match.
In a single elimination tournament, unless you have Pele/fat Ronaldo/Kaka, Zidane/Henry, or David Villa/Xavi/Iniesta, you're better off letting the opponents come to you.