It depends on the situation. My Argonian: Spells-in-Shadows, like many Argonians, prays to the Hist. All are welcomed by the Hist, even the dryskins, should they wish. There's some who disagree, because outsiders usually use the Hist for selfish reasons.

If Spells sees a dead Argonian: "Hear this one's prayer, Great Hist. Help guide this soul back to you, so they may find peace."

Non-Argonian dead: "Whatever gods this soul worshipped, may you welcome him/her back. And should they wish to join with a Hist, may the Hist give them peace.

As a Shadowscale, he naturally has a deep, if a little fearful, respect for Sithis. But when he comes across a Hist in his travels, he'll ask for a long, healthy, life. As well guidance during troubled times.

@Kiara Prayer doesn't necessarily equal worship. Argonians could be seen as agnostic (or atheistic), because they have no god(s). However, they have respect for Sithis and the Hist, but in general, don't worship either. So the prayers you do for quests are done out of necessity, not worship of that deity.

My characters are very devoted to Mara and Stendarr, otherwise I delete them. Even the Dunmer.

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My dunmer prays to Azura for guidance and strength. He is a devoted Azura worshipper and he mostly prays "aloud" to her in moment of doubt or hardship

My Namira worshipping Bosmer thanks the lady of rot and decay before every meal for the gift of disregard that allows her to remain unnoticed by society.
I avoid quests where my character prays to other deities and if I don't I regard that as not-canon ^^

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Courts of Chaos hear my plea!
Great and Most Terrible Lord Sheogorath in your infinite Madness, grant your protection to this lesser child of your house and her fellowship, may our journey run smooth and may our enemies underpants turn to cheese, we place ourselves in your Avuncular Care until the Day of Jyaggld come.

My main wasn't terribly religious until she went to Craglorn and met the Celestials. Now she's a devout Star-Gazer. The switch was SO dramatic my Argonian Dragon Knight thought she'd either been put under mind control or picked up a love interest when she started gushing about the lady with eyes like stars and a celestial voice. He was rather irritated to find out after several failed attempts to 'help' that no, she was being quite literal and she'd just found religion.

For his part, he's a Dragonguard agent and very much a Lukiul, having never had opportunity or desire to link with the Hist. Thus he reveres Akatosh and is a little puzzled why other Saxhleel choose to follow entities that don't even have scales.

My Templar is a Priest of the Eight, spreading their teachings in Pact territory under the Tribunal's noses; he gets away with it through a combination of a very good sword arm and the fact that they have their hands full with other things at this point in history.

My Nightblade isn't terribly religious ATM. My alt Sorceress lives in the Shivering Isles with her vampire collection so of course she considers herself a subject of Sheogorath. And while my new Warden's beliefs aren't set in stone yet, I'm leaning toward making her a follower of the Hungry Cat, aka Hircine.

No one. Gods are lesser beings compared to the Amaranth. They can be killed; just ask Lorkhan. What then sets them above mortals?

It's more like she's the answer to a certain prayer.

"Sweet Mother, sweet Mother, send your child unto me, for the sins of the unworthy must be baptized in blood and fear."

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HAIL DAEDRA!

Aside from my Argonian I have a Khajiit, who prays to Mara and Khenarthi (Khajiit version of Kynareth), Jone and Jode, and is apart of "The Two Moons' Dance" monastery.

I have a Nord, that I RP as a demiprince (offspring of a Daedric Prince or Lord and a mortal). His mother-- a devout worshipper of Hircine, asked the Daedric Prince to sire her a son. So, my Nord worships daddy Hircine. Werewolf form is his true form, human a magical disguise.