Roberts:

- "[T]his Court is not a legislature. Whether same-sex marriage is a good idea should be of no concern to us. Under the Constitution, judges have power to say what the law is, not what it should be."

- "The fundamental right to marry does not include a right to make a State change its definition of marriage."

- "Supporters of same-sex marriage have achieved considerable success persuading their fellow citizens—through the democratic process—to adopt their view. That ends today. Five lawyers have closed the debate and enacted their own vision of marriage as a matter of constitutional law. Stealing this issue from the people will for many cast a cloud over same-sex marriage, making a dramatic social change that much more difficult to accept."

- "It is important to note with precision which laws petitioners have challenged. Although they discuss some of the ancillary legal benefits that accompany marriage, such as hospital visitation rights and recognition of spousal status on official documents, petitioners’ lawsuits target the laws defining marriage generally rather than those allocating benefits specifically. The equal protection analysis might be different, in my view, if we were confronted with a more focused challenge to the denial of certain tangible benefits."

Scalia:

- "This practice of constitutional revision by an unelected committee of nine, always accompanied (as it is today) by extravagant praise of liberty, robs the People of the most important liberty they asserted in the Declaration of Independence and won in the Revolution of 1776: the freedom to govern themselves."

- "We have no basis for striking down a practice that is not expressly prohibited by the Fourteenth Amendment’s text, and that bears the endorsement of a long tradition of open, widespread, and unchallenged use dating back to the Amendment’s ratification. Since there is no doubt whatever that the People never decided to prohibit the limitation of marriage to opposite-sex couples, the public debate over same-sex marriage must be allowed to continue. But the Court ends this debate, in an opinion lacking even a thin veneer of law."

Thomas:

- "[T]he majority invokes our Constitution in the name of a 'liberty' that the Framers would not have recognized, to the detriment of the liberty they sought to protect. Along the way, it rejects the idea—captured in our Declaration of Independence—that human dignity is innate and suggests instead that it comes from the Government."

- "Whether we define 'liberty' as locomotion or freedom from governmental action more broadly, petitioners have in no way been deprived of it. Petitioners cannot claim, under the most plausible definition of 'liberty,' that they have been imprisoned or physically restrained by the States for participating in same-sex relationships. To the contrary, they have been able to cohabitate and raise their children in peace."

Alito:

- "The question in these cases, however, is not what States should do about same-sex marriage but whether the Constitution answers that question for them. It does not. The Constitution leaves that question to be decided by the people of each State."

- "To prevent five unelected Justices from imposing their personal vision of liberty upon the American people, the Court has held that 'liberty' under the Due Process Clause should be understood to protect only those rights that are 'deeply rooted in this Nation’s history and tradition.’ ...And it is beyond dispute that the right to same-sex marriage is not among those rights."

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Disclaimer, IANAL - just picked the quotes that stuck out at me in each dissent.

Roberts' and Scalia's central theme was the Court overstepping its bounds and ending the legislative process prematurely. To me Roberts was essentially saying, "You guys are winning this on the legislative front easily, this is not something SCOTUS needs to decide." Thomas' was pretty cryptic and relied on lots of quotes from 18th and 19th century thinkers to define "liberty." Alito appealed to tradition and worried about this outcome producing a rush of lawsuits from religious institutions who were left in a limbo by the decision; he would have preferred state or national legislation that could clarify how this affected religious schools and such.