Objection 1. It seems that all the sacraments are necessary for salvation. For what is not necessary seems to be superfluous. But no sacrament is superfluous, because "God does nothing without a purpose" (De Coelo et Mundo i). Therefore all the sacraments are necessary for salvation.
Objection 2. Further, just as it is said of Baptism (John 3:5): "Unless a man be born again of water and the Holy Ghost, he cannot enter in to the kingdom of God," so of the Eucharist is it said (John 6:54): "Except you eat of the flesh of the Son of Man, and drink of His blood, you shall not have life in you." Therefore, just as Baptism is a necessary sacrament, so is the Eucharist.
Objection 3. Further, a man can be saved without the sacrament of Baptism, provided that some unavoidable obstacle, and not his contempt for religion, debar him from the sacrament, as we shall state further on (68, 2). But contempt of religion in any sacrament is a hindrance to salvation. Therefore, in like manner, all the sacraments are necessary for salvation.
On the contrary, Children are saved by Baptism alone without the other sacraments.
I answer that, Necessity of end, of which we speak now, is twofold. First, a thing may be necessary so that without it the end cannot be attained; thus food is necessary for human life. And this is simple necessity of end. Secondly, a thing is said to be necessary, if, without it, the end cannot be attained so becomingly: thus a horse is necessary for a journey. But this is not simple necessity of end.
In the first way, three sacraments are necessary for salvation. Two of them are necessary to the individual; Baptism, simply and absolutely; Penance, in the case of mortal sin committed after Baptism; while the sacrament of order is necessary to the Church, since "where there is no governor the people shall fall" (Proverbs 11:14).
But in the second way the other sacraments are necessary. For in a sense Confirmation perfects Baptism; Extreme Unction perfects Penance; while Matrimony, by multiplying them, preserves the numbers in the Church.
Reply to Objection 1. For a thing not to be superfluous it is enough if it be necessary either in the first or the second way. It is thus that the sacraments are necessary, as stated above.
Reply to Objection 2. These words of our Lord are to be understood of spiritual, and not of merely sacramental, eating, as Augustine explains (Tract. xxvi super Joan.).
Reply to Objection 3. Although contempt of any of the sacraments is a hindrance to salvation, yet it does not amount to contempt of the sacrament, if anyone does not trouble to receive a sacrament that is not necessary for salvation. Else those who do not receive orders, and those who do not contract Matrimony, would be guilty of contempt of those sacraments.
Source: Summa Theologica (New Advent)