For an "actual" more generalized definition, gods are beings or spirits worshiped as having power over nature and/or human affairs (also known as a deity), and are considered far above humanity. They are usually the central focus of a religion (a system of beliefs and teachings revolving around the belief in and worship of a supernatural power). In some accounts they are also the creator (or creators) of the world, the universe and everything in it - in-universe, in the case of some fictional universes. When it comes to the power level of different types of beings, gods are at the top (often with various power levels if there are multiple gods, both in fiction and real-life religions).
In real-life there are various religions, and the majority of the world's population are religious, and even some non-religious people believe in the existence of a god or gods (theism and deism). Evidence of theism goes back well into human prehistory. More on that can be found here and here.
God or gods are also the origin of the term "miracle"; originally the term for an extraordinary and welcome event that defies, or is inexplicable, by natural or scientific laws and is either proven to be, or attributed to, a divine agency. As a result, divine power fairly often trumps any other power in a fictional story (and real-life, depending on what one believes), and is the only thing in fantasy that trumps magic.
There are cases, including in some belief systems, of people or things being mistaken for gods that aren't, or masquerading as gods. Given the inherent authority in godhood, some people use the claim for personal gain, out of extreme arrogance or both.
Gods in Fantasy and Science Fiction
Eru Ilúvatar- Supreme creator of the Lord of the Rings universe, though much of creation was actually done by his lesser creations, the Ainur.
Crom- Chief god of the Cimmerian pantheon, Conan invokes his name often. Doesn't really listen to prayers as he despises weakness.
The Elder God- An entity in the Legacy of Kain videogame series, manages the wheel of fate where all souls go to be reincarnated. Jury's out on whether it is a god, but so far its the most powerful entity encountered in the setting.
Aslan- Basically Lion Jesus in the Narnia series. His dad is the real Big G.
Gods in Warhammer
The 4 Chaos Gods, duh
Sigmar- The man turned god, patron of the Empire.
The old world pantheon of Humans- Various deities worshiped by Humans, most notable probably being Ulric whose cult gets to vote on who becomes Emperor, and was also worshiped by Sigmar. Another notable one is Morr, god of death and the afterlife who may also have gone by the name Usirian.
Gork (or is it Mork?)-Brutal but kunnin'.
Mork (or is it Gork?)-Kunnin' but brutal.
The Spider God- Worshiped by Forest Goblins. Likes spiders.
The Dwarf Ancestor Gods- The first dwarfs, ancestors to the whole race. The most high-profile ones are Grungni, Grimnir and Valaya.
Hashut- Likes bulls and bronze.
The Elf pantheon- The various deities of the Elves, notable ones include Asuryan, King of the Gods, Isha, the goddess of healing, fertility, and the harvest, and Khaine, the god of war and murder.
The Horned Rat- The big fucking rat god of the Skaven. Is a huge jerk.
The Great Maw- Giant mouth worshiped by Ogres.
The Lizardmen worshipped the Old Ones as gods, only some of which are known.
Gods in D&D
Pretty much every setting has some sort of fantasy pantheon, since gods are usually required for clerics and paladins to get their God-given powers. Still, some manage to put a twist on the typical formula.
The Forgotten Realms have a truly ridiculous amount of gods, with each race (except humans) having their own pantheon. The only one of real interest, however, is the Faerunian pantheon. That's where you have Mystra, Helm, Deneir and all the other cool guys. The only time the gods really did anything unusual was that one time they came down to solve their petty squabbles in Faerun.
Athas of the Dark Sun setting is an interesting variation in that it's one of the very few settings where gods very definitely don't exist. Depending on the setting you prefer, they either noped straight outta there when they saw how fucked up the world was or were all killed by the primordials. In their absence, clerics get their power from the elemental planes.
On Gothic Earth there is no character class linked to deities, unless one decides to count the antagonistic Red Death as a deity, which would make all spellcasters so to a degree. The sole divine caster class, Mystic, draws their power from understanding the spirit world. Gothic Earth is still Earth however, so all religions around in the late 1800s do exist there, just without mechanical power. By contrast, D&D's other Urban Fantasy setting, Urban Arcana, allows any deity from Earthly religion to grant spells to faithful, but also allows the same of deities of Shadowkind that have fallen to Earth. Dark Matter, which D&D briefly adopted as a campaign setting, features "functional religion" as a provable enough fact and has magic from both dark cults and a Christian secret society explicitly exist (with other sources presumable). Unlike arcane magic, divine magic is not fully documented and replicateable on demand, at least not by the Hoffman Institute that serves as the default viewpoint/PC employer.
Eberron leaves it mainly ambiguous, as the gods don't really act directly. Ever, so they might not exist. Clerics and paladins do get magical powers, but it stems from belief, not actual God-given poets. This works so that even followers of religions known out of character to be scams, like Cults and Path of Inspiration, can get spells, as can Heretics.