Catholic
The Catholic Church teaches that sacred images — of Christ, Mary, and the saints — may be displayed and honored in churches, following the Second Council of Nicaea. It holds that the honor shown to an image passes to its prototype, and that images proclaim the gospel and stir devotion.
Source: CCC 1159–1162; 2131–2132 ↗
Orthodox
The Orthodox Church teaches that icons are windows into heaven and a confession of the incarnation — because God truly became visible, he can truly be depicted. It holds, with the Seventh Ecumenical Council, that icons are venerated but never worshiped, and that rejecting them denies the full reality of Christ's humanity.
Source: The Orthodox Faith, Vol. II — Icons ↗
Lutheran
Lutherans permit images and religious art in churches as adiaphora — things neither commanded nor forbidden — useful for instruction and remembrance. They hold that images must never become objects of worship or be thought to carry spiritual power in themselves.
Source: Formula of Concord, Solid Declaration, Art. X ↗
Reformed
The Reformed tradition rejects images of God — including images of Christ — in worship as a violation of the second commandment. It holds that God is to be worshiped spiritually, and that images inevitably corrupt worship by turning minds from the living God to the work of human hands.
Source: Westminster Confession 21.1–2; Larger Catechism Q.109 ↗
Baptist
Baptists generally make no use of icons in worship, teaching that God is spirit and is to be worshiped without images. They hold that religious art may illustrate biblical stories, but that no image is to receive religious honor.
Source: Baptist inference from BFM 2000, Art. I ↗
Methodist
Methodists generally do not use icons in worship, though religious art such as crosses and stained glass is common. They hold that worship is directed to God alone, and that images may aid devotion but must never become its object.
Source: Articles of Religion, Art. XIV ↗