Here are the majority and minority opinions, as reported by CNN:

"The recitation that ours is a nation 'under God' is not a mere acknowledgment that many Americans believe in a deity. Nor is it merely descriptive of the undeniable historical significance of religion in the founding of the Republic. Rather, the phrase 'one nation under God' in the context of the Pledge is normative. To recite the Pledge is not to describe the United States; instead, it is to swear allegiance to the values for which the flag stands: unity, indivisibility, liberty, justice, and -- since 1954 -- monotheism. The text of the official Pledge, codified in federal law, impermissibly takes a position with respect to the purely religious question of the existence and identity of God. A profession that we are a nation 'under God' is identical, for Establishment Clause purposes, to a profession that we are a nation 'under Jesus,' a nation 'under Vishnu,' a nation 'under Zeus,' or a nation 'under no god,' because none of these professions can be neutral with respect to religion."
-- Judge Alfred T. Goodwin, majority opinion for himself and Judge Stephen Reinhardt

"[L]egal world abstractions and ruminations aside, when all is said and done, the danger that 'under God' in our Pledge of Allegiance will tend to bring about a theocracy or suppress somebody's beliefs is so minuscule as to be de minimis. The danger that phrase presents to our First Amendment freedoms is picayune at most... upon Newdow's theory of our Constitution, accepted by my colleagues today, we will soon find ourselves prohibited from using our album of patriotic songs in many public settings. 'God Bless America' and 'America The Beautiful' will be gone for sure, and while use of the first and second stanzas of the 'Star Spangled Banner' will still be permissible, we will be precluded from s traying into the third. And currency beware! Judges can accept those results if they limit themselves to elements and tests, while failing to look at the good sense and principles that animated those tests in the first place."
-- Judge Ferdinand F. Fernandez, dissenting opinion