Miranda Bailey is assumed to follow a Christian set of beliefs. When asked by a patient if she believed in God, she replied that she had to believe. Additionally, she sometimes prays before surgeries. She also mentions Jesus as being the "control" in her life or the guidelines to what she does.
Preston Burke is very spiritual and follows a Christian set of beliefs. He celebrates Christmas.
George O'Malley was Catholic, but was chastised by his mother for getting a divorce (despite the fact that the marriage was in a Church of Elvis).
Derek Shepherd is from an Irish-Catholic background, but he has not talked about any religious beliefs. He does mention having held onto his sister when their father was shot and "praying for God to help them" in the season 7 episode Superfreak, other than that he hasn't mentioned being overtly religious.
Amelia Shepherd doesn't think any God would make such an evil world, as explained in Private Practice season 3 episode In the Name of Love. She explicitly says there she's not religious and doesn't believe in God. Then in the season 5 finale of Private Practice, she tells her dying baby as she kisses him goodbye, "Your father's waiting for you. His name is Ryan, and he's waiting for you. So you won't be lonely." which heavily implies she believes in Heaven at that point. In Grey's Anatomy season 11 episode She's Leaving Home she yells at the "Universe" rather than a god. In All I Could Do Was Cry, Amelia lights a candle in the chapel and advises others to do the same but does not pray for the Kepner-Avery baby/family the way other characters do. However, earlier in season 11, in Staring at the End, Amelia explains about Dr. Herman's cancer: "It's not just a tumor. It's ingenuity. It's strength. It's adaptability. It's poetry. It's one of God's masterpieces. It is alive." and then in the season 14 premiere, when Amelia is told about a different patient, "That tumor's inoperable," she replies "I'm not a big believer in inoperable. God, yes. Unicorns, possibly. Inoperable, no." So Amelia's stance on God is perhaps inconsistent throughout the two series.
Callie Torres was raised Catholic. She can quote the Bible, as shown during the fight with her father about her sexuality. Before her divorce from George, Callie believed in God, but she lost faith, only believing in love. Later in season 5, she revealed she believed in God again sometimes.
Cristina Yang was raised in a Jewish faith upon her mother's remarriage. However, she stopped believing in "that kind of stuff" as soon as she was old enough to know better.
April Kepner has a strong born-again Christian faith. Many of her decisions stemmed from her Christian faith, including wanting to withhold sex until she was married, which she ultimately failed to do and instead she lost her virginity to Jackson before they got married in season 10. Her faith comes up a lot with the birth of her child and her marriage.
Naomi Bennett is Catholic, as she expressed concern over her divorce with Sam when they had to pay a house call to a convent.
Addison Montgomery is a WASP. She only ever attends church at Christmas and only discovered how to pray when Callie taught her how to when her brother had to have brain surgery. She explains in Private Practice season 5 episode God Laughs that she has complicated feelings about God but does still believe.
Jackson Avery doesn't believe in God but does believe in medicine and helping people. After April’s accident, he prayed for her and during Jo and Alex’s wedding, he talked about growing his faith.
Richard Webber can be presumed to follow a Christian set of beliefs. In the voice over for I Want You With Me, he mentions praying to God and he got married by a priest in the hospital chapel.
Owen Hunt references a belief in God in Sleeping Monster. In Readiness is All, he asks April to pray when they're in a life threatening situation because he knows she's someone who does that. In Cold As Ice, when April's life is in jeopardy, he insists everyone in the O.R. pray. He doesn't care how everyone does it or who they do it to, but he knows April would want them to pray for her.
George's funeral: Many of George's colleagues attended his Catholic funeral.
Praying for April and Jackson's Baby: Not knowing how to show their support, all of April and Jackson's close colleagues went to the hospital's chapel to light a candle for them, and some of them even prayed. Jackson himself also went to the chapel and "prayed" for God to show up for April.