"Archon" means "leader" or "leading". There are a few types of "Archontes". To be an "Archon" means to have been officially tonsured by the Ecumenical Patriarchate. The honour itself is also called an "offikion" in other words a "recognition of status or achievement".

Archons or Archontes Psaltai of the Great Church of Christ (or of the Ecumenical Patriarchate): These are the four main psaltai of the Patriarchal church. The two psaltai of the right choir are called Archon Protopsaltis (the main psaltis) and Archon First Domestikos (his helper). The two psaltai of the left choir are called Archon Lambadarios (the main psaltis) and Archon Second Domestikos (his helper). The leading young psaltis of the right choir is called Protocanonarchos (but he is not an Archon). A full list of Archontes Protopsaltai, Lambadarioi and Domestikoi is given in Angelos Boudouris' article in Orthodoxia Magazine (1937) available on Analogion [pdf, 7Mb].

Archon Protopsaltis of the Holy Archdiocese of Constantinople: These are psaltai honoured for the performance practice contribution outside of the Patriarchate. To date the following people have been honoured Archontes Protopsaltai:

Chrysanthos Theodosopoulos
Athanasios Karamanis
Harilaos Taliadoros
Angelos Margaritis
Lykourgos Angelopoulos
Lykourgos Petridis
Antonios Aristodemou (Australia)
Nikolaos Nikolaidis (Sweden)
Evangelos Nanakos
Dimitrios Ioannidis

Archon Music Teacher of the Great Church of Chist (or of the Ecumenical Patriarchate): These are psaltai honoured for their teaching contribution outside of the Patriarchate. To date the following people have been honoured Archontes Music Teachers:

Avraam Efthemiadis
Ioannis Sofroniadis (mentioned in Lykourgos Petridis' Liturgy book)
Vasileios Katsifis
Konstantinos Panas
Diamantis Mavraganis
Stefanos Dontsios
Georgios Tsatsaronis
Angelos Boudouris
Dimitrios Sourlantzis

Archon Teacher of the Apostolos of the Great Church of Christ (or of the Ecumenical Patriarchate): These are psaltai honoured for their performance practice but this officion is less prestigious than "Archon Protopsaltis" above. It is not really clear why this different honour was invented. To date the following people have been given this offikion:

Dimitrios Nerantzis

Archon Hymodist of the Great Church of Christ (or of the Ecumenical Patriarchate): These are psaltai honoured for their performance practice but this officion is less prestigious than "Archon Protopsaltis" above. It is not really clear why this different honour was invented. To date the following people have been given this offikion:

Georgios Hatzihronoglou

Archon Protekdikos of the Great Church of Christ (or of the Ecumenical Patriarchate): Offikion invented (according to Angelos Boudouris) by Georgios Papadopoulos in the late 19th cent. To date the following people have been given this offikion:

Georgios Papadopoulos

Hymnographer of the Great Church of Christ (or of the Ecumenical Patriarchate): These are people who have been distinguished by their composition of liturgical hymns and services. To date the following people have been given this offikion:

Fr. Athanasios Simonopetritis
Fr. Gerasimos Mikragiannanitis
Elias Bogdanopoulos

Archon Protopsaltis of the Holy Archdiocese of America: Similar to Archon Protopsaltis of the Holy Archdiocese of Constantinople, honoured by the Ecumenical Patriarchate but belonging to a different order (see notes below). To date the following people have been given this offikion:

Fotios Ketsetzis (Boston, US)
Matthaios Andreou (Montreal, Canada)

Notes by Dr. Alexander Lingas:
Archons in what used to be the Archdiocese of North and South America are indeed archons of the Ecumenical Patriarchate, just not of the same 'order' as those in Europe. The order of those in the USA is that of St Andrew (see http://www.archons.org/archons/ ), whereas those in Greece (if I remember correctly) are of St Mary Pammakaristos. Now that Canada is an independent metropolis answering directly to the Ecumenical Patriarchate, I'm not sure about where there archons belong. A number of Greek Orthodox liturgical musicians who work in polyphony in addition to or instead of chant have received Patriarchal offikia. The conductor, composer and musicologist Frank Desby was an Archon Lampadarios, as is the composer/conductor Tikey Zes. You can find a full list of current archons on page 140 of the following file http://www.goarch.org/.http://2006.pdf Curiously, Ketsetzis is not listed here, but I found a few more Lampadarioi:

Tykye Camaras, Lambadarios
Elias D. Chinonis, Lambadarios
Philip N. Christopher, Lambadarios

There are also a few church singers hiding out among the other titles, for example:

Theodore Bogdanos, Hartoularios
George T. Demos, Aktouarios
Thomas M. Pallad, Hartophylax

Archon Protopsaltis of the Holy Archdiocese of Australia: Similar to Archon Protopsaltis of the Holy Archdiocese of Constantinople but honoured by the Archbishop of Australia and not the Ecumenical Patriarchate. To date the following people have been given this offikion:

Ilias Frangoulis (Adelaide, Australia)

Archon Protopsaltis of the Patriarchate of Alexandria: Similar to Archon Protopsaltis of the Holy Archdiocese of Constantinople but honoured by the Patriarchate of Alexandria and not the Ecumenical Patriarchate. To date the following people have been given this offikion:

Elias Stavrou (South Africa)

Protopsaltis of the Church of Antioch : Similar to Archon Protopsaltis of the Holy Archdiocese of Constantinople but honoured by the Patriarchate of Antioch and not the Ecumenical Patriarchate. To date the following people have been given this offikion:

Mitri El Murr (Beirut, Lebanon)

Protopsaltis of the Holy Metropolis of Canada: Similar to Archon Protopsaltis of the Holy Archdiocese of Constantinople but honoured by the Metropolitan of Canada and not the Ecumenical Patriarchate. To date the following people have been given this offikion:

Konstantinos Lagouros (Montreal, Canada)

Protopsaltis of the Holy Archdiocese of Cyprus: Similar to Archon Protopsaltis of the Holy Archdiocese of Constantinople but honoured by the Archdiocese of Cyprus and not the Ecumenical Patriarchate. To date the following people have been given this offikion:

Theodoulos Kalinikos (Lefkosia, Cyprus)