Any rock song. It's just so rare to have a rock song in Eurovision. So imagine the awesomeness when Finland won - with a then-record score - with a hard rock song in 2006.
The 2007 edition in Oslo saw Serbia's first participation... and first win in the contest. It's also notable that it won with Marija Šerifović's song "Moltiva", the first non-English song to win Eurovision since the national language rule was lifted in 1999, from which point all the winning songs had been in English until Serbia's entry.
France's entry in 2009, Et s'il fallait le faire by Patricia Kaas. Only one person on stage, hardly any light or stage show, just 2 minutes and 45 seconds of singing followed by a tiny bit of dancing. Listen to the audience reactions.
The butterflies used to show each country's flag in 2013 were beautifully made and just plain epic; they would fly in, land where the country's flag should be right before the country performed their song, and fly away off-screen. The butterflies were also used to present which countries that qualified for the final. There would be a shadow resembling a butterfly, and when a country was revealed, the country's butterfly would appear on that spot. Just see itfor yourself.
2014's winner, Gender Bender and The CutieConchita Wurst, using her victory moment to deliver a short but powerful speech — “This night is dedicated to everyone who believes in a future of peace and freedom. You know who you are — we are unity and we are unstoppable.”
Even before Conchita Wurst, 1998 winner Dana International. At the time of her entry of the contest, there had been no (out) LGBT representatives to the contest before, making her, a transgender woman, a landmark. When she won on the final vote, it suddenly became all the more evident that the LGBT community and Eurovision went hand in hand, and her victory allowed for more LGBT contestants to enter in the years to come. Additionally, to further reach out to the LGBT community, the 2016 finals became the first time the contest was ever broadcast in America, in partnership with the LGBT television channel Logo (and represented by its own gay commentators as well). Prior to that, the Canadian expy of Logo, OUT TV, broadcast the contest a few times.
The 2016 contest is very unique in that many countries that are usually defeated in the semi-final qualified to the final (Croatia, Bulgaria and Czech Republic). Special mention goes to Czech Republic, which qualified for the first time ever.
None of the countries got 0 points in either the semi-finals or finals. The quality of songs overall was the best it has been in a long while.
Bulgaria also got a highly respectable result in the final, with a fourth place. Given that the same artist competed in 2011 without qualifying for the final, this could count as sweet revenge for her.
After the jury voting, Polish performer Michał Szpak was 25th out of 26 with only 7 points. 2 minutes later, Poland jumped to 8th place as "Color of Your Life" was third in the televoting, with 229 points.
Ukraine beating Russia for the win in 2016, especially considering how their song ("1944") is indirectly about the conflict over Crimea, which partially motivated Ukraine to skip Eurovision 2015 in the first place.
Australia coming in second behind Ukraine is a feat in itself as given the sort of geopolitical voting that tends to takes place, Australia coming in second was based on the sheer strength of Dami Im's performance.
The country names in different fonts as song credit backgrounds in the 2016 edition.
In 2017, Portugal dominated and won. Keep in mind, this is not just any country here; they have competed since the 60's and never even finished in the top 5 - and then they just go and win the entire thing. Not just that, they came 1st in the jury and televoting. The adorable singer having a unique demeanor and charisma on stage singing his ballad must have really done it for everyone.
In addition, two countries following behind (Bulgaria and Moldova) were honored to be given their respective best places ever in the contest (Bulgaria 2nd, Moldova 3rd). It's nice to see countries which normally don't get high up and/or even qualify, producing places with which the singers can walk home with pride.
With Moldova in particular, their song scored fairly low in the jury voting, but then pulled up to third place using votes from the televoting alone. Since their song was performed by the same band that had spawned Epic Sax Guy seven years earlier, it can be inferred that Moldova made the top 3 through the power of Memetic Mutation.
Outside of the Big Five, all of the non-English languages qualified to the grand final. This includes "Amar Pelos Dois", Portugal's winning song; "Historyja majho žyccia (Story of My Life)", the first song sung entirely in Belarusian; and "Origo", Hungary's entry sung in Hungarian and performed by the first Romani person to compete for Hungary.