You might've heard of an ambitious Skyrim mod called Religion that completely changes the way you interact with the gods of Tamriel—it's one of the best mods for Skyrim. With the mod installed all your actions, from the crimes you commit to the armor you wear, affects the way individual gods view you, and they can either bless you or curse you as a result. The whole mod has just been overhauled for its version 3.0, adding religious visions and new gods called Ancient Spirits, as well as the 13 Constellations.
It's an incredibly deep system with lots of moving parts, and you can have multiple blessings—or curses—at the same time. All of the gods are looking for different things, and you'll get clues about their desires through visions. To receive visions, you'll first have to worship them at set points in the world, which increases their disposition towards you based on the amount of in-game time you spend worshiping them (don't worry, you can press T to wait if you want to rack up many hours at once).
Once you've worshiped them enough to receive a vision, you'll be able to ask them for guidance or for a boon. But you don't want to ask for a gift too early, because it might annoy some gods, causing them to curse you.
It sounds like it will reward exploration and investigation. You'll have to read books related to the gods to find out exactly what they want, and respond with your actions accordingly. Blessings gradually get more powerful as disposition increases, and some are specific to each god: if Julianos likes you enough they'll let you cast spells without using magicka, or if you worship the Daedric Lord Azura then you might gain invulnerability.
Displeasing the gods through your actions can also make you cursed. The Nine Divines, in general, won't like it if you commit crimes. If you wrong enough people, they might decrease your health, magicka and stamina regeneration for a period of time. Daedric curses are more imaginative. If you ask Malacath for help but they "they don't find you amusing enough", you'll receive a curse that means you're blamed for every crime committed in Skyrim.
I like that it's not completely transparent: you can tell a lot about what each god wants from the lengthy descriptions on the mod's Nexus page, but you'll still have to find out more if you want their blessings.
If you're interested, you can download the mod for Skyrim Special Edition here. The 3.0 version for regular Skyrim is here. It's still in beta, so expect some rough edges and some missing content—creator IronDusk33 is working hard to complete it all.