Ecumenical Councils are those to which the bishops, and others entitled to vote, are convoked from the whole world (oikoumene) under the presidency of the pope or his legates, and the decrees of which, having received papal confirmation, bind all Christians. A council, Ecumenical in its convocation, may fail to secure the approbation of the whole Church or of the pope, and thus not rank in authority with Ecumenical councils. Such was the case with the Robber Synod of 449 (Latrocinium Ephesinum), the Synod of Pisa in 1409, and in part with the Councils of Constance and Basle.

(extracted from the Catholic Encyclopedia )

The college of bishops exercises power over the universal Church in a solemn manner in an ecumenical council. But there never is an ecumenical council which is not confirmed or at least recognized as such by Peter's successor (CCC #884).
As far as Catholics are concerned there are 21 (twenty-one) ecumenical councils.

1. First Council of Nicaea (AD 325)

Contra Arianism (who denied the divinity of Jesus) and declared that Jesus is homoousios meaning "of the same substance" or "one in being" with the Father.
formulated the Creed and fixed the date of Easter

2. First Council of Constantinopel (AD 381)

Contra Macedonius (who challenged the divinity of the Holy Spirit) and declared that the Divinity of Holy Spirit and thus completed The Creed

3. Council of Ephesus (AD 432)

Defined the true personal unity of Christ against that of Nestorius and declared Mary as theotokos, literally means "God bearer" but transliterated as "Mother of God".

4. Council of Chalcedon (AD 451)

Contra Eutyches who believed in single nature (monophysite) of Jesus and declared that Jesus has two natures (divine and human) which come together "without confusion or change, without division or separation" to form the one undivided person of Jesus.

The Assyrian Orthodox Church of the East accept the first, second and fourth councils. The Eastern Orthodox Churches (Armenian, Coptic, Ethiopian, Syrian Jacobites and Syrian Malankara) accept the first, second and the third councils (they are also referred as non-Chalcedonian churches). However they do not adopt the monophysite view either.

5. Second Council of Constantinopel (AD 553)

Condemned the errors of Origen and certain writings (The Three Chapters) of Theodoret, of Theodore, Bishop of Mopsuestia and of Ibas, Bishop of Edessa.
Confirmed the first four general councils, especially that of Chalcedon whose authority was contested by some heretics.

6. Third Council of Constantinopel (AD 681)

Contra Monothelitism (which believes that Jesus has only one will) and declared that Jesus has both divine and human will.

7. Second Council of Nicaea (AD 787)

legalized Veneration of icons and distinguished between veneration and adoration , the latter is meant for God alone.

The Eastern Orthodox Church recognizes these seven councils as ecumenical councils.

8. Fourth Council of Constantinopel (AD 869)

Consigned to the flames the Acts of an irregular council (conciliabulum) brought together by Photius against Pope Nicholas and Ignatius the legitimate Patriarch of Constantinople.

9. First Lateran Council (1123)

Abolished the right claimed by lay princes, of investiture with ring and crosier to ecclesiastical benefices and dealt with church discipline and the recovery of the Holy Land.

10. Second Lateran Council (1139)

Put an end to the errors of Arnold of Brescia.

11. Third Lateran Council (1179)

Condemned the Albigenses and Waldenses and issued numerous decrees for the reformation of morals.

12. Fourth Lateran Council (1215)

Issued an enlarged creed (symbol) against the Albigenses (Firmiter credimus), condemned the Trinitarian errors of Abbot Joachim.
Declared the term transubstantiation to describe the Real Presence in the Eucharist.

13. First Council of Lyons (1245)

excommunicated and deposed Emperor Frederick II and directed a new crusade, under the command of St. Louis, against the Saracens and Mongols.

14. Second Council of Lyons (1274)

It effected a temporary reunion of the Greek Church with Rome. The word filioque was added to the symbol of Constantinople and means were sought for recovering Palestine from the Turks. It also laid down the rules for papal elections.

15. Council of Vienne (1311)

Dealt with the crimes and errors imputed to the Knights Templars, the Fraticelli, the Beghards, and the Beguines, with projects of a new crusade, the reformation of the clergy, and the teaching of Oriental languages in the universities.

16. Council of Constance (1414-1418)

Put an end to the schism by the election of Pope Martin V, which the Council of Pisa (1403) had failed to accomplish on account of its illegality. The rightful pope confirmed the former decrees of the synod against Wyclif and Hus.

17. Council of Basle-Ferrara-Florence (1431-1443)

Union with the Greek Church was effected, the Greeks accepting the council's definition of controverted points.

18. Fifth Lateran Council (1512-1517)

Its decrees are chiefly disciplinary. A new crusade against the Turks was also planned, but came to naught, owing to the religious upheaval in Germany caused by Luther.

19. Council of Trent (1545-1563)

contra Reformation and reaffirmed the Catholic belief in seven sacraments; justification by faith shown by the fruit of faith, good works or charity; revelation of God through both Bible and Holy Tradition; Mass as perpetuation or re-presentation of Jesus one sacrifice on Calvary.

20. First Vatican Council (1870)

Besides important canons relating to the Faith and the constitution of the Church, the council decreed the infallibility of the pope when speaking ex cathedra,

21. Second Vatican Council (1962-1965)

adaptation to modern needs

Reference:

1. Dwyer, E.J. (1993): Bringing Churches Together, An Introduction to Ecumenism, Gideon Goosen, Australia.

2. Schreck, A. (1987): The Compact History of the Catholic Church, Servants Books, USA.