From the 2010 General Introduction to the Roman Missal:
“68. The Creed is to be sung or said by the Priest together with the people on Sundays and Solemnities. It may be said also at particular celebrations of a more solemn character.”
The Roman Missal’s Order of Mass, n. 19, allows either the Nicene or Apostles Creed at any Mass.
The Creed is optional when there are the Scrutinies, (prayers for the elect who are to be baptised a few weeks later.) From the book Rite of Christian Initiation of Adults: “… then, if required, the profession of faith is said. But for pastoral reasons these general intercessions and the profession of faith may be omitted.” (RCIA, n. 143, 157, 164 edition for Australia and England, n. 156, 170, 177 in the editon for the USA.).
The usual time for the Scrutinies is the Third, Fourth and Fifth Sundays of Lent. But it can be done at other times during the year, except Solemnities. (USA RCIA, n. 146, Australia RCIA n. 133).
At the Easter Vigil there is a renewal of baptismal promises, instead of the Creed.
The Creed is not said if there is a baptism in the Mass. (Rite of Baptism for Children, n. 29, The Rites Volume One, Liturgical Press, 1990, ISBN: 0-8146-6015-0, page 374).
And if there is a confirmation at Mass, from the Rite of Confirmation (Rite of Confirmation, n. 31. The Rites Volume One, Liturgical Press, 1990, ISBN: 0-8146-6015-0, page 492).
Nor if there is an ordination of a deacon, priest or bishop in the Mass, from the rite of “Ordination of Deacons, Priests and Bishops” (The Rites Volume Two, Liturgical Press, 1991, ISBN: 0-8146-6037-1, pages 28, 39, 66).
Nor if there is a consecration to a life of virginity in the Mass: (The Rites Volume Two, Liturgical Press, 1991, ISBN: 0-8146-6037-1, page 161, 177).
Nor if there is a rite of religious profession in the Mass,
for a temporary profession by a man: (The Rites Volume Two, Liturgical Press, 1991, ISBN: 0-8146-6037-1, page 213).
the same for a perpetual profession by a man, n. 52(b), page 221.
same if a man renews his vows, n. 83(b), page 233.
same for a women, temporary profession, 25(b), page 252.
same for a women, perpetual profession, 57(b), page 258.
same for a women, renewal of vows, 90(b), page 272.
Nor if there is a blessing of an abbot (The Rites Volume Two, Liturgical Press, 1991, ISBN: 0-8146-6037-1, page 304.)
Same for the blessing of an abbess, n. 10, page 314.