Mine is Oben Thundersmith, A Blonde arrogant Tempest cleric. 

Hi, I have Drutar, a half orc cleric 

Ah! An excuse to show off one of the characters on my list (number 4 out of 14, pray for me), the archaeologist Raine Esden, vHuman Tempest Cleric of the god of moments and murderer of his best friend!

Apparently his backstory is similar to a cross between that of Wayne (Mistborn era 2) and Aaron Burr (Hamilton).

His build focuses on both WIS and DEX in order to effectively use arcing blade from Magic Initiate.

Blue Jay is a gnomish cleric of Nebelun whose keen attention to detail is matched only by her severe social anxiety.

Ulfgar Oakenfall, my Level 9 Hill Dwarf Life Cleric.

Mad Magnar (see sig)

He fell in battle with King Grol and was taken by the mists to Ravenloft. He has sworn to avenge himself on the Bugbear but is currently trapped by the Domains of Dread. 

Mine is Sarris, my level 3 Wood Elf cleric of Life

Barddek Gloomguide: Undertaker of Clan Lutgher; Servant of Kelemvor; Underdark guardian of Deadthorn and Argentum; Slayer of undead. (Level 6 after playing through some portion of Out of the Abyss)

Backstory here: 

Barddek's family has been the caretakers of those sent to the afterlife for generations. More specifically, his family are both undertakers and cemetery caretakers for his clan, Clan Lutgehr, ensuring their fellow dwarves pass on to the next world painlessly and without worrying about gravediggers or worse. Barddek is happy go lucky, always has a smile on his face, and is friendly and outgoing with most everyone. That being said, he has seen the worst humanity, and the undead, have to offer and while outgoingly jovial, is overly suspicious and cautious around folk he doesn't know. Barddek, like all Dwarves, loves his alcohol and dabbles in using interesting ingredients to try to find new and flavorful variations of his favorite drinks.

Skrie Tripfoot is a halfling Trickster Cleric. She is the chosen of a trickster goddess and is more scout/sniper/rogue than a cleric -- healing comes more as an afterthought than her main purpose, but she hasn't lost a teammate yet. 

Ulfric Ironhammer, of the Ironhammer clan. A devout Dwarf driven towards the life of a cleric of Berronar by the loss of his brother in a surprise attack deep in his native mines, Ulfric now adventures, determined to be strong enough to one day return and prevent such a loss happening again. Best known in my party for absolutely clutching some tough combats we were losing with his uncanny ability for perfectly timed Nat 20s.

Auriana Seyres, a human, grave domain cleric who is a devotee to Kelemvor.  She was originally based in the small temple of Kelemvor in the lower city of Baldur's Gate, but with rise of the dragon cult, and the rumors swirling about them raising undead dragons, she was tasked to infiltrate the cult to learn what she can about their activities, so she can work with the other faithtful of Kelemvor to stop them.

I have never played a cleric but I want to. I have several character ideas.

A lizardfolk or yuan-ti cleric who serves Xolotl, the dog-headed aztec god of death, lightning, fire, deformaties, and axolotls. Xolotl was also buddies with quezlcoatl and helped him rescue humanity, and he piloted the dead across the river of the dead and to the underworld. He would probably be a grave domain cleric that specializes in hunting down the undead that have escaped death. He could also be a tempest domain cleric but I don't know what his goals would be. 

Probably a triton but maybe a halfling life cleric who serves the Porpoise of Life, my homemade magical porpoise with incredible healing and life giving powers. He was once a sailor who was terribly wounded by pirates or a storm or something and he fell in the sea, about to die, when the Porpoise of Life came and rescued him. He vowed to serve the Porpoise from then on and bring his restorative magic to those who dwell on the land, far from the reaches of a Porpoise. He also is terrified of sailing because of the shipwreck he was in and will avoid the sea at all costs. But he is still proud of his seafaring days and will often tell tall tales of his adventures in the ocean.

My cleric is Life Domain, Holy Person Variant Aasimar named Shei-Lya

A lawful evil human trickery cleric named Aravose who is secretly the bbeg to my party.

Do half Clerics count? If so, meet Peregrine, my Aarakocra Way of the Kensei Monk / War Domain Cleric:

As the only lawful good character in a… less than lawful Icewind Dale party he was a lot of fun to play as being an earnest, naive but always trying to do the right thing cleric/monk.

He more than held his own in most fights, while having just enough support abilities and spellcasting to remain useful out of combat as well. With the Monk's Ki-fuelled Attack and War Domain's War Priest feature he could throw out three full weapon attacks most turns, which was especially good for his longbow, though with his speed he would rarely stay at range, preferring to zoom in to help take the heat off allies etc.

A lot of fun to play.

Ferra Kuldjargh is an Arcana Domain cleric that holds reverence towards (and acts on behalf of) the Weave as a sort of "force of nature". She narrowly escaped the apocalypses by her organizations use of chronomancy and conjuration magic to propel her to another timeline where she could act to prevent it from occurring (by working with the party). 

So, this cleric arose out of the need for a new character when my first character for the campaign died. My first character was also named Ferra Kuldjargh and was a Battlerager/Armorer multiclass (angry dwarf with full body spiked armor). Since I wanted to play an Arcana domain cleric and time-based shenanigans were already used in the campaign's world, I thought it would be funny for a gentler, alternate version of Ferra to take the original's place.

That being said, the hot blooded attitude of barbarian Ferra will sometimes still pop out, as the Weave connects the souls of cleric Ferra and her other, alternate lives. Usually I play off this idea when I cast Spirit Guardians with the "guardians" appearing like multiversal versions of Ferra or when I cast Summon Celestial reflavored to be summoning the might of barb Ferra's soul back into service. 

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Hi, I have Drutar, a half orc cleric 

 Same

Mathias of The Gilded Spade

Human, Grave Domain

He is well dressed in black silk vestments over polished bronze scale mail engraved with ancient scriptures edged within a honeycomb pattern. He dons an ornate bronze death masque during ceremonies and to cleanse the unholy. From his belt you see he carries a bronze battle aspergillam mace, mass bells and a small glass lantern like reliquary which hangs from an iron chain and contains a floating blind embalmed eye within the amber honey of the mellified St. Klytus. (Eye of St. Klytus). A continual flame lights his path upon his head when vetting tombs of undead and thieves. 

Mathais, Psalmaturge of the Gilded Spade (currently Level 11)

Brother Heliodorus, who has long since given up his birth name, spent the early years of his life in a bustling city, surrounded by the noise and chaos of urban living. However, as he grew older, he felt a growing disconnect from the materialistic and worldly pursuits of the city. This led him to seek solitude and spiritual enlightenment away from civilization. Leaving the city behind, Heliodorus sought refuge in a secluded cave high in the mountains, where he spent many years in quiet contemplation and communion with nature.

During this time as a hermit he honed his connection to the sun to the extent that even in the utter darkness of the cave he could feel the light of the sun and call it forth. Heliodorus seeks to spread the light of the sun's blessing and is not at all annoying about it even though he brings it up d20 times per day.

Shava - Eladrin cleric of twilight domain