For me, one of the most moving celebrations of Yom Haatzmaut was from the 62nd Yom Haatzmaut in 2010 on Mount Hertzl. The particularly moving parts were when the speaker recited Psalms 137 and 126 immediately followed by a dance performance as a chorus sang a song written to the tune of the chorus Va pensiero from Verdi's Nabucco.
The significance of Psalms 137 and 126 are obvious in terms of the connection of the Jewish people to the Land of Israel, the former of mourning for its loss and the latter of celebrating the return. However, the opera chorus requires some background. The original tune reflects reflects Italian nationalism from the mid-nineteenth century—expressed as Italians yearning for a free country in the manner of the Hebrew exiles in Babylon yearning to return to Zion.
Using that tune hearkens back to a time when the connection between the Jewish people and the Land of Israel was a given in European consciousness. Drawing on that theme, the Israeli version combines the themes of Psalms 137 and 126, starting with recollection of the time in exile as in the line "Kinnorot b'dimah cheresh talinu (We hung our harps in tears and silence)." It continues with anticipation of redemption, "N'nucham b'vinyan migdaleha (We will be comforted in the building of her towers)," and finishes with the return of the exiles, "V'yashuvu p'zureha k'vatchilla b'shirat g'ulla (And her scattered ones will return as in the beginning with a song of redemption)."