I think the only religion/god we know of in Runeterra is the Spider God Elise worships. And that isn't even an actual god, it's a physical being that is simply being worshiped.
So, are there any other religions or gods/ ancient forces in Runeterra? Maybe Anivia is one of them?
Demacia is modeled after medieval European fantasy, so some sort of Catholicism-like religion is probably existing. Kayle is listed as affiliated with Demacia, so she can be some sort of divine messenger there, she keeps mentioning "afterlife". Noxus probably falls within the same cultural circle - Morgana is a "fallen angel" after all. They are most likely two sides of the same coin, although Noxus is leaning a bit too much towards "Camp Evil" stereotype, so if we were to take things realistically, religion either isn't a big thing there or doesn't have any influence on Noxian politics and experiments with black magic. I think the Orthodox church would be a possible parallel here - it was never as dominating in Russia as Catholicism was in Italy.
Freljord is obviously Norse fantasy, so Nordic-esque pantheon is a given. People of Freljord surely share common beliefs with the Vikings (glory in death in battle).
Ionia is very loosely based on East Asia, with heavy Japanese and Chinese influence (architecture, island country, yin/yang design of old Karma). Since it's designed from a Western perspective, it's gonna be a mixture of Buddhism and Shintoism (much like the cartoon "Avatar").
Mt. Targon is a peculiar one - it's a monotheistic religion with an opposing sub-group. Solari is dominating but Lunari used to be a thing. I'd actually say it has very little parallel to our world, since for the Solari the Moon is not evil, but worshipping it over the Sun is heresy. Best example I can come up with would be Islam - they believe that Jesus was a prophet, and worshipping him as a god is blashpemy.
Shurimian lore doesn't mention any religions, but since it's based on stereotypical "desert lands" theme, one of two main themes is possible: politeism (Mesopotamia, Egypt) or monotheism (Zoroastrianism). The commonly found Egyptian tropes (Nasus, Renekton, Azir) confirm the Egyptian influence.
Shadow Isles are easy - a death cult. These are commonly found in RPG settings.
Bilgewater is leaning towards "ghost stories", "sailor tales" and possibly even "voodoo" with Shadow Isles as an important factor, full blown Pirates of the Caribbean. That means no organized religions, but some sort of shamanism.
As for Piltover and Zaun, they're enlightened secular societies where religion isn't probably a major factor.
A much better question than "Are there any religions in Runeterra?" would be "What is religion in a world where magic exists?". It's a very good theological question present in various fantasy settings, especially if in many cases religion transponds to magic. What is particularly interesting is that word magic derives from Persian magi ("priest"), and up until the 20th century pretty much all supernatural powers in literature were connected to religion (in Western literature, either divine blessing or demonic curse).
Main approaches to this topic in fantasy are:
uhm there are the solari/lunari who worship the sun/moon respectively(ok the lunari are currently more like a cult) and there is also shurima that seemingly worhsipped the sun. and yes it has been confirmed that the sun/moon are supernatural beings in this setting as they were shown to bestow power upon people that worship them.
There is also Lissandra who worships the watchers and malzs cult that worships the void,not to mention Karthus who worships death.
diana moon.
leona sun ppl.
kayles angel worshippers.
there are tons of religions.
and 
both have pretty terrifying cults if that counts for anything.
