Iron Man
Atheist
From Iron Man issue #1: "Have you ever believed in something? I always had trouble. When my parents tried to tell me about Santa Claus, I just thought 'Gee--that guy's business model has got to be unsustainable.' And God? Oh, me and gods. I mean, I've met a few, and I still don't believe in them. Side-stepping precise definition of belief: tedious evidence, empiricism, pedantry and so on and so boring... There's only two things I ever managed to believe in. Firstly, myself. And even then, only about 50% of the time. Secondly, the future. That there would be one, and we'd make it."
Spiderman
Protestant
it has always been apparent that Peter Parker (Spider-Man) is from a Protestant Christian background. Parker's precise denominational affiliation has never been made clear. Peter Parker has never been depicted as a regular churchgoer and could probably not be said to be religiously observant on a daily basis in any organized way. Nevertheless, Parker has exhibited a clear belief in God from time to time, and his Protestant Christian background has always been strongly manifest in his behavior and personal code of ethics.
Thor
Agnostic
This one likely comes as a shock to the reader. However, there is strong evidence for it. There was a memorable issue of Namor (written and drawn by John Byrne), in which Namor the Sub-Mariner was on trail. Thor was one of the witnesses. The bailiff naturally hesitated when it came time to swearing Thor in on a Bible, but Thor said he had no problem acknowledging a greater God, and we was quite willing to be sworn in just as anybody regular person would be.
In an old Pre-Korvac Avengers story, Thor is with the Avengers when they walk into a church. Thor admits he is uncomfortable because he knows that the God of that church doesn't think much of old Thor. Thor admitted that neither he nor Odin actually claim any sort of supremacy, but that many members of the church find Thor to be offensive. The point seemed to be that Thor does not consider himself a "God" in the same sense that most contemporary monotheists use the word.
Captain America
Christian
Captain America has always been portrayed as a solidly Protestant character. He is a bastion of mainstream American values and "boy-next-door" qualities. Captain America's mainstream religious beliefs, including his faith in God and broadly accepted American religious values, are an integral part of his character.
It was explicitly stated in Ultimates 2 that Captain America attends church every Sunday. This version of the character is part of Marvel's "Ultimate" imprint, and not part of original mainstream Marvel continuity. But the Ultimate Captain America character is a close analogue to the original version of the character. The religious beliefs and religious affiliation of the two versions of the character are essentially the same, but we are unaware of any explicit references within mainstream continuity stating that Captain America attends church services with such frequent regularity.
The Hulk
Catholic
For many readers, any lingering questions about whether "mainstream" Dr. Banner is also Catholic might disappear when they recollect that Dr. Banner married a Catholic nun (or at least a novitiate). From the time the "Hulk" was introduced, the love of Dr. Banner's life was Betty Ross. At a time when she thought he was dead, she joined a convent and began training to become a nun. Later she learned that Dr. Banner was alive and she left the full-time religious life. Possibly Betty Ross did not complete her training and initiation to the point that she was a full-fledged nun, but the point is, if Betty was sufficiently Catholic to become (or almost become) a nun, she was probably Catholic enough to want to marry a fellow Catholic.
The Thing
Jewish
The character's name, Benjamin Jacob Grimm, is certainly a Jewish one. But during the 1960s (and for a long time afterward), there was a strong taboo in comics and many other popular entertainment mediums against referring to real-world religious affiliations of major characters. It was not until four decades later that The Thing's Jewish identity was revealed. The revelation occurred in Fantastic Four (Vol. 3) #56, published in August 2002, in a story titled "Remembrance of Things Past"), written by Karl Kesel, pencilled by Stuart Immonen, and inked by Scott Koblish.
Green Lantern (Hal Jordan)
Possibly Catholic
Hal Jordan is one of the most famous and one of the most overtly religious major superheroes in the DC Universe. Yet Hal Jordan's religiosity has essentially never been portrayed as participation in traditionally recognized Earth-based religious denominations.
With regards to Hal Jordan's religious affiliation in the traditional sense a very strong case can be made that the character is Catholic. A case can also be made that the character is Jewish, although the evidence for this seems less substantial. For both possibilities, there are readers who believe that Hal Jordan practiced his religious faith at least somewhat as an adult. Based on the available evidence and the nature of Jordan's religious observance as an adult, it is quite possible that Jordan is a Jewish Catholic.
Wonder Woman
Greco-Roman Classical Religionist
The religious affiliation of Wonder Woman, also known as Princess Diana, can be classified as Greco-Roman classical religion.
Since this influential comic book super hero character was first created by polygamist feminist psychologist William Moulton Marston in 1941, Wonder Woman's origins and continuing storylines have been tied intricately to Greco-Roman mythology. The ancient Greek and Roman pantheon consisting of Zeus, Hera, Poseidon, Hades, Athena, etc. have always been rendered as explicitly real in Wonder Woman's universe. This pantheon is also known as the Olympians, or the gods of Olympus, named after Mount Olympus, the mountain in Greece which was until recently their home.
Superman
Methodist
Clark Kent was raised as a Methodist. While growing up in Smallville, Kansas, Clark Kent attended Sunday church services at the local Methodist church with his mother, Martha Kent, every week until he was fourteen years old. These aspects of the character are not speculative, but are canonical - established by in-continuity published DC Comics. Action Comics #850 (August 2007), for example, identifies Methodism by name as the denomination that Clark Kent and his mother attended.
Jonathan also raised his adopted son with staunch Protestant values, but Jonathan has never been much of a churchgoer. Clark stopped attending church services when his super-hearing, X-ray vision and other super senses began developing. As Clark later told his wife, Lois Lane, he stopped attending services becaues he "knew too much about their lives -- their problems -- their lies... [he] was afraid" that he might lose his faith in people. So he decided to distance himself from such close-contact, frequent congregational worship and put his faith in "the best that humanity has to offer" (Action Comics #849, July 2007).
Batman
Episcopalian
Bruce Wayne is usually portrayed as Episcopalian (including in comics by writer and Quora member Elliot S Maggin), although some writers such as Frank Miller have portrayed him as Catholic. It is usually assumed he is somewhat lapsed, but there are repeated markers such as Christian gravestones and occasional references to prayer that he has not totally abandoned his childhood faith.
Wolverine
Skeptic
Wolverine was for many years one of Marvel's most mysterious characters, as he had no memory of his earlier life and the origins of his distinctive Adamantium skeleton and claws. Like much about the character, his religious affiliation is uncertain. It is clear that Wolverine was raised in a devoutly Christian home in Alberta, Canada. His family appears to have been Protestant, although this is not certain. At least into his teen years, Wolverine had a strong belief in God and was a prayerful person who strived to live by specific Christian ethics and moral teachings.
Over the many decades since he was a child and youth in 19th Century Alberta, Wolverine's character has changed significantly. It is safe to say that Wolverine, at his core, is now something of a cynic and a skeptic.