Objection 1. It would seem that we ought not to pray for others. On praying we ought to conform to the pattern given by our Lord. Now in the Lord's Prayer we make petitions for ourselves, not for others; thus we say: "Give us this day our daily bread," etc. Therefore we should not pray for others.
Objection 2. Further, prayer is offered that it may be heard. Now one of the conditions required for prayer that it may be heard is that one pray for oneself, wherefore Augustine in commenting on John 16:23, "If you ask the Father anything in My name He will give it you," says (Tract. cii): "Everyone is heard when he prays for himself, not when he prays for all; wherefore He does not say simply 'He will give it,' but 'He will give it you. '" Therefore it would seem that we ought not to pray for others, but only for ourselves.
Objection 3. Further, we are forbidden to pray for others, if they are wicked, according to Jeremiah 7:16, "Therefore do not then pray for this people... and do not withstand Me, for I will not hear thee." On the other hand we are not bound to pray for the good, since they are heard when they pray for themselves. Therefore it would seem that we ought not to pray for others.
On the contrary, It is written (James 5:16): "Pray one for another, that you may be saved."
I answer that, As stated above (Article 6), when we pray we ought to ask for what we ought to desire. Now we ought to desire good things not only for ourselves, but also for others: for this is essential to the love which we owe to our neighbor, as stated above (25, 1 and 2; 27, 2; 31, 1). Therefore charity requires us to pray for others. Hence Chrysostom says (Hom. xiv in Matth.) [Opus Imperfectum, falsely ascribed to St. John Chrysostom]: "Necessity binds us to pray for ourselves, fraternal charity urges us to pray for others: and the prayer that fraternal charity proffers is sweeter to God than that which is the outcome of necessity."
Reply to Objection 1. As Cyprian says (De orat. Dom.), "We say 'Our Father' and not 'My Father,' 'Give us' and not 'Give me,' because the Master of unity did not wish us to pray privately, that is for ourselves alone, for He wished each one to pray for all, even as He Himself bore all in one."
Reply to Objection 2. It is a condition of prayer that one pray for oneself: not as though it were necessary in order that prayer be meritorious, but as being necessary in order that prayer may not fail in its effect of impetration. For it sometimes happens that we pray for another with piety and perseverance, and ask for things relating to his salvation, and yet it is not granted on account of some obstacle on the part of the person we are praying for, according to Jeremiah 15:1, "If Moses and Samuel shall stand before Me, My soul is not towards this people." And yet the prayer will be meritorious for the person who prays thus out of charity, according to Psalm 34:13, "My prayer shall be turned into my bosom, i.e. though it profit them not, I am not deprived of my reward," as the gloss expounds it.
Reply to Objection 3. We ought to pray even for sinners, that they may be converted, and for the just that they may persevere and advance in holiness. Yet those who pray are heard not for all sinners but for some: since they are heard for the predestined, but not for those who are foreknown to death; even as the correction whereby we correct the brethren, has an effect in the predestined but not in the reprobate, according to Ecclesiastes 7:14, "No man can correct whom God hath despised." Hence it is written (1 John 5:16): "He that knoweth his brother to sin a sin which is not to death, let him ask, and life shall be given to him, who sinneth not to death." Now just as the benefit of correction must not be refused to any man so long as he lives here below, because we cannot distinguish the predestined from the reprobate, as Augustine says (De Correp. et Grat. xv), so too no man should be denied the help of prayer.
We ought also to pray for the just for three reasons: First, because the prayers of a multitude are more easily heard, wherefore a gloss on Romans 15:30, "Help me in your prayers," says: "The Apostle rightly tells the lesser brethren to pray for him, for many lesser ones, if they be united together in one mind, become great, and it is impossible for the prayers of a multitude not to obtain" that which is possible to be obtained by prayer. Secondly, that many may thank God for the graces conferred on the just, which graces conduce to the profit of many, according to the Apostle (2 Corinthians 1:11). Thirdly, that the more perfect may not wax proud, seeing that they find that they need the prayers of the less perfect.
Source: Summa Theologica (New Advent)