Letter to the Smyrnaeans

The Eucharist is the true participation in the Body and Blood of Jesus Christ.  Here he directly challenges the Docetists who found no reason to celebrate the Eucharist since they denied the humanity of Christ:

Let no one be deceived! Even the heavenly powers and the angels in their splendor and the principalities, both visible and invisible, must either believe in the Blood of Christ, or else face damnation. Let him grasp it who can. Let no rank puff up anyone; for faith and love are paramount--the greatest blessings in the world. Observe those who hold erroneous opinions concerning the grace of Jesus Christ which has come to us, and see how they run counter to the mind of God! They concern themselves with neither works of charity, nor widows, nor orphans, nor the distressed, nor those in prison or out of it, nor the hungry or thirsty.

From Eucharist and prayer they hold aloof, because they do not confess that the Eucharist is the Flesh of our Savior Jesus Christ, which suffered for our sins, and which the Father in His loving-kindness raised from the dead. And so, those who question the gift of God perish in their contentiousness. It would be better for them to have love, so as to share in the resurrection. It is proper, therefore, to avoid associating with such people and not to speak about them either in private or in public, but to study the Prophets attentively and, especially, the Gospel, in which the Passion is revealed to us and the Resurrection shown in its fulfillment. Shun division as the beginning of evil.

You must all follow the lead of the bishop, as Jesus Christ followed that of the Father; follow the presbytery as you would the Apostles; reverence the deacons as you would God's commandment. Let no one do
anything touching the Church, apart from the bishop. Let that celebration of the Eucharist be considered valid which is held under the bishop or anyone to whom he has committed it. Where the bishop appears, there let the people be, just as where Jesus Christ is, there is the Catholic Church. It is not permitted without authorization from the bishop either to baptize or to hold an agape; but whatever he approves is also pleasing to God. Thus everything you do will be proof against danger and valid. (paragraphs 6-8)

Comments from the Catechism of the Catholic Church:
Paragraph 1369
The whole Church is united with the offering and intercession of Christ. Since he has the ministry of Peter in the Church, the Pope is associated with every celebration of the Eucharist, wherein he is named as the sign and servant of the unity of the universal Church. The bishop of the place is always responsible for the Eucharist, even when a priest presides; the bishop's name is mentioned to signify his presidency over the particular Church, in the midst of his presbyterium and with the assistance of deacons. The community intercedes also for all ministers who, for it and with it, offer the Eucharistic sacrifice: 

       Let only that Eucharist be regarded as legitimate, which is celebrated under [the presidency of] the bishop or him to whom he has entrusted it. (St. Ignatius of Antioch, Ad Smyrn. 8:1; SCh 10, 138.)

       Through the ministry of priests the spiritual sacrifice of the faithful is completed in union with the sacrifice of Christ the only Mediator, which in the Eucharist is offered through the priests' hands in the name of the whole Church in an unbloody and sacramental manner until the Lord himself comes. (PO 2 # 4)

Letter to the Ephesians

The Eucharist should be central to our lives and our worship:

Make an effort, then, to meet more frequently to celebrate God's Eucharist and to offer praise. For, when you meet frequently in the same place, the forces of Satan are overthrown, and his baneful influence is neutralized by the unanimity of your faith. Peace is a precious thing: it puts an end to every war waged by heavenly or earthly enemies. (paragraph 13)

Here St. Ignatius focuses on 1 Corinthians 10:17:

If Jesus Christ, yielding to your prayer, grants me the favor and it is His will, I shall, in the subsequent letter which I intend to write to you, still further explain the dispensation which I have here only touched upon, regarding the New Man Jesus Christ--a dispensation founded on faith in Him and love for Him, on His Passion and Resurrection. I will do so especially if the Lord should reveal to me that you--the entire community of you!--are in the habit, through grace derived from the Name, of meeting in common, animated by one faith and in union with Jesus Christ--who in the flesh was of the line of David, the Son of Man and the Son of God--of meeting, I say, to show obedience with undivided mind to the bishop and the presbytery, and to break the same Bread, which is the medicine of immortality, the antidote against death, and everlasting life in Jesus Christ. (paragraph 20)

Comments from the Catechism of the Catholic Church:
Paragraph 1404-1405
The Church knows that the Lord comes even now in his Eucharist and that he is there in our midst. However, his presence is veiled. Therefore we celebrate the Eucharist "awaiting the blessed hope and the coming of our Savior, Jesus Christ," (Roman Missal 126, embolism after the Our Father: expectantes beatam spem et adventum Salvatoris nostri Jesu Christi; cf. Titus 2:13) asking "to share in your glory when every tear will be wiped away. On that day we shall see you, our God, as you are. We shall become like you and praise you for ever through Christ our Lord." (EP III 116: prayer for the dead)

There is no surer pledge or dearer sign of this great hope in the new heavens and new earth "in which righteousness dwells,"  (2 Pet 3:13) than the Eucharist.  Every time this mystery is celebrated, "the work of our redemption is carried on" and we "break the one bread that provides the medicine of immortality, the antidote for death, and the food that makes us live for ever in Jesus Christ." (LG 3; St. Ignatius of Antioch, Ad Eph. 20, 2: SCh 10, 76)

Letter to the Romans

The Prince of this world is resolved to abduct me, and to corrupt my Godward aspirations. Let none of you, therefore, who will then be present, assist him. Rather, side with me, that is, with God. Do not have Jesus Christ on your lips, and the world in your hearts. Give envy no place among you. And should I upon my arrival plead for your intervention, do not listen to me. Rather, give heed to what I write to you. I am writing while still alive, but my yearning is for death. My Love has been crucified, and I am not on fire with the love of earthly things. But there is in me a Living Water, which is eloquent and within me says: "Come to the Father." I have no taste for corruptible food or for the delights of this life. Bread of God is what I desire; that is, the Flesh of Jesus Christ, who was of the seed of David; and for my drink I desire His Blood, that is, incorruptible love. (paragraph 7)

Letter to the Philadelphians

The unity of the Church is found in the Eucharist.  St. Ignatius equates the Eucharistic celebration to a sacrifice complete with altar: 

Take care, then, to partake of one Eucharist; for, one is the Flesh of  Our Lord Jesus Christ, and one the cup to unite us with His Blood, and one altar, just as there is one bishop assisted by the presbytery and the deacons, my fellow servants. Thus you will conform in all your actions to the will of God. (paragraph 4)