Eagle

Because it soars upward, the eagle is a symbol of the resurrection or ascension of Christ. By extension, the eagle symbolizes baptized Christians, who have symbolically died and risen with Christ.

Especially when the eagle has a halo (as in the image above), it is the symbol of John the Evangelist. The eagle represents John because of his lofty and "soaring" gospel (it is much more theological in nature than the other three).

Related Bible Verses

But those who hope in the Lord will renew their strength. They will soar on wings like eagles; they will run and not grow weary, they will walk and not be faint. (Isaiah 40:31)

Their faces looked like this: Each of the four had the face of a man, and on the right side each had the face of a lion, and on the left the face of an ox; each also had the face of an eagle. (Ezek. 1:10)

Image Gallery

St. John symbolized by an eagle, with the first words to the Gospel of John in his beak (fresco, Velemer Church, 1378).	John as the eagle, clutching in his beak the first words to the Gospel of John in Latin (stained glass, St. Mary's Church, Oxford).
Agnus Dei and Four Evangelists - eagle bottom right (9th century ivory, Met Museum).

References

1. Color illustration by Walter E. Gast.
2. Patricia S. Klein, Worship without Words: The Signs and Symbols of Our Faith (2000).
3. Carolle E. Whittenmore, ed., Symbols of the Church.
4. W.E. Post, Saints, Signs, and Symbols.
5. George Wells Ferguson, Signs & Symbols in Christian Art.
6. Frederick Rest, Our Christian Symbols.