Four new cantons have been created, and two new provinces by splitting some other cantons away from their former provinces. I've updated the HASC and NUTE codes to show the new provinces, but I haven't yet added the new cantons to the list, since I don't have their ancillary data. This page on the INEC  (Instituto Nacional de Estadística y Censos) website has links to maps of the cantons by province.

Mario Pezza sent a spreadsheet with canton populations from the 2001 census, areas, and capitals. I have added them to the table below, taking the opportunity to update the list with some minor spelling changes and one newly created canton.

Ecuador is divided into provinces, which are subdivided into cantons. The table below shows 216 cantons, complete as of the 2001 census.

Ecuador Online  has maps of every province, showing the cantons.

Change history:

1. ~1992: According to the CIESIN  site, the following cantons were created between about 1990 and 1994. In Azuay province, Chordeleg canton was split from Gualaceo; El Pan and Sevilla de Oro cantons were split from Paute; Oña canton was split from Nabón. In Bolívar province, Las Naves canton was split from Guaranda. In Cañar province, Déleg canton was split from Azogues; El Tambo canton was split from Cañar. In Chimborazo province, Cumandá canton was split from Alausí. In Cotopaxi province, Sigchos canton was split from Latacunga. In Esmeraldas province, Atacames canton was split from Esmeraldas. In Guayas province, Coronel Maridueña and Simón Bolívar cantons were split from Yaguachi; La Libertad canton was split from Salinas; Lomas de Sargentillo and Nobol cantons were split from Daule. In Los Ríos province, Buena Fe canton was split from Quevedo. In Manabí province, Pedernales canton was split from Sucre. In Morona-Santiago province, Huamboya canton was split from Palora; San Juan Bosco canton was split from Limón Indanza. In Napo province (now Orellana), Loreto canton was split from Archidona. In Pastaza province, Santa Clara canton was split from Pastaza. In Pichincha province, Pedro Vicente Maldonado and San Miguel de los Bancos cantons were split from Quito. In Zamora-Chinchipe province, El Pangui canton was split from Yantzaza.
2. (There may be more changes between 1994 and 2000 that I don't know about.)
3. The name of Urbina Jado canton in Guayas province was changed to Salitre. San Vicente canton was created in the province of Manabí. Both of these changes are recent, probably in the period 1997-2000.
4. 2001-10-18: Pablo Sexto canton split from Huamboya (former HASC code EC.MS.HU). Pablo Sexto is often written "Pablo VI".
5. 2002-03-28: Camilo Ponce Enríquez canton split from Pucará canton in Azuay province.
6. 2002-10-23: Tiwintza canton created in Morona-Santiago province; Paquisha canton split from Centinela del Cóndor canton in Zamora-Chinchipe province.
7. 2007-10-02: Santo Domingo de los Colorados canton, but not its capital city, renamed Santo Domingo de los Tsáchilas. Canton transferred from Pichincha province to the new Santo Domingo de los Tsáchilas province. The canton's new NUTE code should be 30123001.
8. 2007-11-07: La Libertad, Salinas, and Santa Elena cantons transferred from Guayas province to the new Santa Elena province. Their new NUTE codes should be 30224002, 30224003, and 30224001, respectively.
9. 2007-11-20: Quinsaloma canton split from Ventanas canton in Los Ríos province.
10. 2007-11-26: La Concordia canton created in Esmeraldas province.
11. 2013-05-31: La Concordia canton moved from Esmeraldas province to Santo Domingo de los Tsachilas.

Other names of subdivisions:

1. Francisco de Orellana: Orellana (variant)
2. Pablo Sexto: Pablo VI (variant)
3. Pelileo: San Pedro de Pelileo (variant)
4. Píllaro: Santiago de Pillaro (variant)
5. Salitre: Urbina Jado (obsolete)
6. Santo Domingo de los Colorados: Santo Domingo (variant)
7. Veinticuatro de Mayo: 24 de Mayo (variant)
8. Yaguachi: San Jacinto de Yaguachi (variant)
9. Yantzaza: Yanzatza (variant)