Mythological figures who have saved the world at least once:
The Abrahamic god:
There are probably too many characters fitting these requirements, to count. Most gods are depicted as saving the world on at least one occasion. The Abrahamic (i.e., Judeo-Christian-Islamic) god saved the world from a flood, albeit a flood of his own creation, and according to Christian belief, he later saved humanity again by sending his son/self to earth, so that he could be sacrificed for the sins of humankind.
The Chinese archer-god, Yi, The Time of the Ten Suns (c. 1027-220 BCE)
The ancient Chinese apparently believed that there were once ten suns. They usually took turns lighting up the sky, but at some point, they decided (or were commanded, depending on which version of the myth you read) to rise into the sky simultaneously. The earth became unbearably hot, of course, and the effects of the drastic increase in temperature were catastrophic: Crops withered away in the fields, lakes, ponds, and even oceans began to dry up, and animals and humans were forced to seek shelter from the stifling heat. Seeing the disaster unfolding on the earth, the gods dispatched a divine archer named Yi, or Houyi, who proceeded to shoot down 9 of the 10 suns. As he was about to shoot down the tenth, and final, sun, he was reminded that the earth needs at least one sun to survive, so he relented. By preventing the earth from being consumed by fire, he saved the world.
Old Coyote, The Great Fire - Patwin Tribe (Northern California) myth, date of origin unknown
A spurned lover wants vengeance for the two women who rejected his affection, and therefore, builds a boat, sets the world on fire, and rows out to sea. Old Coyote sees the conflagration and leaps into action.
But the fire burned with terrible speed. It ate its way into the south. It licked up all things on earth, men, trees, rocks, animals, water, and even the ground itself.
Now Old Coyote saw the burning and the smoke from his place far in the south, and he ran with all his might to put it out. He put two little boys in a sack and ran north like the wind. He took honey-dew into his mouth, chewed it up, spat on the fire, and so put it out. Now the fire was out, but there was no water and Coyote was thirsty. So he took Indian sugar again, chewed it up, dug a hole in the bottom of the creek, covered up the sugar in it, and it turned to water and filled the creek. So the earth had water again.
But the two little boys cried because they were lonesome, for there was nobody left on earth. Then Coyote made a sweat house, and split a number of sticks, and laid them in the sweat house over night. In the morning they had all turned into men and women.
Thus, Old Coyote stopped the worldwide blaze, brought water back to the earth, and ensured that humanity would survive the disaster.
Great Flood Myths:
Assorted - Almost ubiquitous, but the most notable accounts come from the Middle East; the first incarnations probably date back to prehistoric times.
This needs little explanation. We're all familiar with the story of Noah, and most of us know that Noah was based on earlier versions of stories built around the same premise, most notably the Epic of Gilgamesh. The stories actually go back quite a bit farther than that, though, and have probably been told for as long as stories about anything have been told. The central concept is obvious and well known: a global flood is imminent, and all life will be wiped out in the deluge; a divine or supernatural entity, however, warns a special individual or family, which has been chosen to survive the disaster, usually because they, unique among humans, are deemed worthy of salvation for some reason (sometimes they are especially pious, sometimes the person being saved is a great king or priest, sometimes it is simply someone who the gods like more than everyone else).
The special person or people gather together a number of animal species, herd them onto an implausibly large boat, and weathers the storm at sea, until finally, the waters recede and the people and animals can repopulate the world.
Many of these stories are so similar that it seems like only the names have been changed: in Hebrew mythology, the special person is Noah; in the Babylonian Epic of Gilgamesh, the special person is Utnapishtim; in the Sumerian myth, the special person is King Ziusudra, or sometimes King Atrahasis. The rest of these stories, by and large, are nearly identical.
Greek mythology has its own variant of the great flood narrative: We all know the famous story of Prometheus, in which the Titan known, rather predictably, as Prometheus, steals fire from the gods of Mount Olympus, and gives it to mortal men, thus incurring the wrath of the gods, especially Zeus. In some versions of this myth, Zeus throws a tantrum, sending a global deluge to drown the planet. Prometheus learns of Zeus' plans, and warns his son Deucalion of the impending flood. Deucalion builds a boat, hurries his family aboard, and they alone survive the cataclysm, and later go on to repopulate the earth. This version of the myth is almost certainly based on much older oral traditions, but was famously published by the Roman poet Ovid in his magnum opus, Metamorphoses, in the year 8 CE.
There is, however, an interesting, and quite unique, variation of the flood myth, which comes to us from ancient Egypt: The sun god, Ra, fears that mankind is plotting to overthrow him, and therefore sends the goddess Hathor, who is called the "Eye of Ra", to wipe out the human race entirely. She begins to carry out his orders, and soon, she has killed so many people that the blood that has been shed gathers together and forms a massive tidal wave, flooding the land across the entire world. Seeing this, Ra begins to have some second thoughts, and eventually decides that killing everyone in the world is a bit much. He tells Hathor to stop, but she is pretty much insane by this point, and ignores him. She is filled with wild bloodlust, and therefore begins to drink the lakes and oceans of blood she has already shed. Ra realizes that he needs to rein this crazy broad in, so he commands his slaves to brew a ridiculous amount of beer, pour it into one of the basins Hathor has just drained, creating a literal lake of beer, and then dye it red so Hathor thinks it is actually more blood. She falls for the trick, guzzles down a lake-full of beer, and passes the eff out. Thus, in what might be the greatest story ever told, one god stops another god from destroying the world, by tricking her into drinking millions of gallons of beer. I always knew that beer would eventually save the world, but I had no idea that it had already happened.
Mythological figure who has saved the world repeatedly (and before anyone else did so):
However, you asked for characters who save the world on a routine basis, repeatedly coming to the rescue throughout history. This being the case, we would do well to look towards what is probably the most ancient mythology still extant in the world - Hinduism. Specifically, we will be looking at the myths associated with the supreme deity of Hindu belief, known primarily as Vishnu, although he goes by many other names, including Krishna.
The first reference to Vishnu is found in one of the oldest texts in the world, the Rig Veda, where he is depicted as a solar deity, quite impressive in its own right, but merely a shadow of the greatness which would later be attributed to him. Regarding the age of the Rig Veda:
The Rigveda's core is accepted to date to the late Bronze Age, making it one of the few examples with an unbroken tradition. Its composition is usually dated to roughly between c.1500-1200 BCE. Philological estimates tend to date the bulk of the text to the second half of the second millennium. Being composed in an early Indo-Aryan language, the hymns must post-date the Indo-Iranian separation, dated to roughly 2000 BC. A reasonable date close to that of the composition of the core of the Rigveda is that of the Indo-Aryan Mitanni documents of c. 1400 BC. Other evidence also points to a composition close to 1400 BC.
Gradually, he became a much more powerful and important figure, and eventually rose to prominence as the savior of the world in general, and humanity in particular.
From the site "Religion Facts"
In Hinduism, Vishnu, whose name means "All-Pervading," is the protector of the world and the restorer of moral order (dharma). He is peaceful, merciful, and compassionate. To Vaisnavites, Vishnu is the Supreme Lord.
Vishnu is often shown reclining or asleep as he awaits the next annihilation and renewal of the world.
Vishnu is best known through his ten avatars (incarnations), which appear on earth when there is disorder in the world. Rama and Krishna, whose stories are told in the Epics and the Puranas, are the most popular incarnations of Vishnu by far. [Note: See below for more information about the avatars of Vishnu]
Curiously, the interpretative saga of Lord Vishnu begins with Lord Shiva. Once when man's wickedness overran all restraining boundaries, an infuriated Shiva transformed himself into a wrathful form known as Bhairava. Thus converted, Shiva began his rampage of destruction, killing, maiming, and ripping out hearts of humans and drinking blood, his menacing laughter thundering all around.
On behalf of humanity, Vishnu approached Bhairava and requested him to stop the slaughter. Bhairava said: "I will go on killing until my bowl is filled with enough blood to quench my thirst." It was common knowledge that Bhairava's bowl could never be filled and his thirst never quenched.
His heart filled with compassion, Vishnu addressed Shiva thus: "Let me give you all the blood you need. You don't have to bleed mankind." So saying, Vishnu struck his forehead with his sword and let his blood spurt into Bhairava's bowl. Ages passed, Vishnu kept pouring his blood into the bowl, while Bhairava kept drinking it.
Bhairava finally realized that Vishnu was sacrificing himself for the sake of the world. Moved by Vishnu's generosity, he declared, "So long as you preserve the world, I will not seek to quench my thirst. But when the world becomes so corrupt that even you cannot sustain it, I will raise my trident and squeeze every drop of blood from the heart of man."
Thus, as exemplified in the above legend, Vishnu is the Preserver, the protector of all humanity. A deity who saves mankind from calamities which result from its own foibles.
Each of the incarnations of Vishnu have saved, or will save, the world.
According to Hindu belief, Vishnu has incarnated on Earth at least nine times to destroy evil and restore justice in the world. His major manifestations or avatars are as follows:
Matsaya (fish) In this form Vishnu saves the Vedas, the Hindu texts containing all the knowledge of the world, from massive floods that threaten the earth [and saves the world, and much of humanity - although probably not the people who had recently converted to Buddhism, which pissed the Hindus off a bit - as well].
Kumra (tortoise) As a tortoise, Vishnu recovers the valuable things that were lost at the bottom of the ocean during the floods, including the nectar of immortality.
Varaha (boar) When Vishnu incarnates as Varaha, he battles the demon Hiranyakashyap, who pulled the earth to the bottom of the ocean. Varaha dives into the depths of sea and brings the earth back to safety.
Narasimha (a being with the head and claws of a lion and the body of a man) In this incarnation, Vishnu finally kills the demon Hiranyakashyap, who had become a powerful tyrant threatening humankind as well as the gods.
Vamana (dwarf) As the sage Vamana, Vishnu conquers King Bali, a demon who had seized control of heaven, earth, and the netherworlds.
Parashurama (fierce warrior) In this sixth incarnation, Vishnu uses his axe to kill Kartavirya, a king with a thousand arms who stole Parshurama’s father’s holy calf.
Rama (a king and ideal man) Lord Rama is the seventh incarnation of Vishnu and the main character in the classic Hindu epic the Ramayana. Lord Rama represents righteousness, truth, and strength of character. This avatar isn’t known for a single mission or triumph, but for holding on to his ideals in the face of many challenges. Rama has been given the status of a god by Hindu followers.
Krishna (deity) Like Rama, Lord Krishna is also revered as a god in the Hindu faith. However, Krishna is seen as more playful, endearing, and accessible than Lord Rama, who personifies perfection. There are many tales about Krishna’s pranks and love escapades with the cow maidens. As the eighth incarnation of Vishnu, Krishna is also the protagonist in another Hindu epic, the Mahabharata. At a very young age, Krishna slays a number of powerful demons, including Kansa, the king of the snakes. According to tradition, Krishna is the only incarnation of Vishnu who was aware of his divine powers from infancy. For this reason, Krishna is commonly equated with Vishnu rather than being considered only an earthly incarnation.
In Hinduism, some branches of thought hold that Gautama Buddha is the ninth incarnation of Vishnu, while others state that Balarama, Krishna’s brother, is the ninth avatar. The following is a brief description of both possible avatars.
Buddha, whose name means “the awakened one” was born as Siddhartha, a prince destined for a life of ease and luxury. However, Siddhartha eventually goes on a long quest for knowledge, attains enlightenment and from then on is known as the Buddha. He spends the rest of his life spreading his message of peace and inner wisdom, which is the foundation of Buddhism.
Balarama (also called Baladeva) is known for his extraordinary strength and prowess in warfare, using mace and his plough as weapons. In addition, he is famous for his loyalty and protection of Krishna. Those who believe that Balarama is the ninth avatar of Vishnu worship him as a god who helps people find transcendent bliss.
Kalki (the prophesied god) In Hindu mythology, the tenth avatar of Vishnu has not yet appeared on Earth, but it is said that he will come to destroy evil and restore the moral order of humanity by the end of the Kali Yuga period, the current era in the Hindu calendar. Since we are only 5,000 years into Kali Yuga, which is said to last 432,000 years, it may be a long time before the Kalki avatar appears.
Although there may have been mythological figures who repeatedly saved the world prior to the traditions regarding Vishnu, we don't know anything about them. As far as extant texts are concerned, everything that superheroes do, Vishnu did first. People have been listening to stories about him and his exploits for at least 3,500 years, and probably much, much longer - the oral traditions might could conceivably go back 5,000 years or more. Remarkably, and unlike most other ancient myths, a huge number of people still believe in, and worship, Vishnu today - probably more than a billion people, in fact.
In light of all of these facts, it would appear that Vishnu was the first entity to come to humanity's rescue, time and time again, and what's more, he'll be back to save us all again in about 427,000 years, this time in his tenth and final incarnation, whom Hindus refer to as Kalki.