Different versions of Superman at different times in his 75 year history touted him as the Last Son of Krypton. And other versions of the character would include literally millions of survivors he was not initially aware of being held captive in the Bottle City of Kandor.
In the Golden Age
Early adventures of the Golden Age Superman had him, for at least a while, being the only survivor of his lost home planet of Krypton. But by the Silver Age of comics no one counted on the popularity and longevity of this strange immigrant from the stars.
Eventually, he would get a cousin (Kara Zor-l/Power Girl who debuts in All-Star Comics #58, 1976). She survived Krypton but was sent to Earth in a slower rocket. She would not arrive on Earth until after Kal-L had reached adulthood. He welcomed her, trained her in the use of her metahuman abilities and even allowed her to replace him on the Justice Society when he retired.
His only other interaction with Kryptonians came in the form of the only Kryptonians he ever fought with. U-ban, Mala and Kizo, three brothers formerly of Krypton's Science Council were sent into exile (by Jor-L, of course) for attempting to control all the water on Krypton.
In the Silver Age
Silver Age Superman was an all-together different character. He would have an entire family of human, metahuman, and alien friends who would become his surrogate family. Superman became family friendly and the tragedy of Krypton's demise was less in the spotlight. The stories were lighter, more fun and often didn't always make a lot of sense.
Silver Age Superman had a cousin as well, Kara Zor-El and her origins were almost the same as Power Girl's but she was a much less strident character and even adopted variations on her cousin's costume. The Superman Family included: The Kents, Jor-El and Lara, the journalist of the Daily Planet, the Superpets, Krypto the dog, Streaky the cat, Beepo the monkey, and Comet the Horse, Lori Lemaris, the Legion of Superheroes and the recurring non-menaces Mister Mxyzptlk and Bizarro.
During the Silver Age and thereafter, different continuities will eventually have Superman confront the evil genius Brainiac. Brainiac managed to create a device capable of shrinking an entire city and all of its inhabitants small enough to fit inside a bottle.
Later rewrites will have Brainiac become a machine-intelligence spawned on Krypton. In any case, Brainiac was inadvertently responsible for the entire vast city of Kandor and its 6 million inhabitants being able to survive the destruction of Krypton. This becomes one of the most famed artifacts in the Superman Mythos: The Bottle City of Kandor.
During the Silver Age Kal-El would even acquire a collection of Kryptonian superpets (who looked exactly like their Terran equivalents...) complete with intelligence and superhuman powers similar to Superman's. This has not been repeated in later eras except for the creation of Krypto, the Last Dog of Krypton.
Over time, other survivors would be less welcome. Kal-El learned about the Phantom Zone projector and its White Zone, where prisoners of the former Krypton placed the worst of their criminal element. These terrifying villains would escape the Phantom Zone and periodically wreck havoc. In some realities, they would escape the Phantom Zone and kill every living thing on Earth. The most famous of these commonly called "Phantom Zone villains" were General Dru-Zod, Faora Hu-Ul, and Jax-Ur. There were easily two or three dozen of these reprobates held in the Phantom Zone.
During the Silver Age: The bottle city of Kandor is eventually placed on a planet called Rokyn and restored to its normal size. The Kandorians renamed their city as New Krypton. (v1 Superman # 338, 1979.08)
In the Modern Age, Post-Crisis
In the early Post-Crisis stories, the editorial fiat decreed Superman was "the last son of Krypton. During John Byrne's Man of Steel run, there would be no other Kryptonians. They held to this for about a decade.
The Bottle City would once again reappear in the Post-Crisis Universe. As in the previous continuity, the Kandorians were held prisoner by Brainiac, and were kept under a red-sun emulator, preventing the Kandorians from developing any superhuman powers unless released from the city.
In the Pre-Flashpoint iteration of the DC Universe, the Kandorians are released from the bottle and establish New Krypton, a planet on the opposite side of our sun. This time, let's just say it doesn't end well for the former Kandorians. (See: Superman: War of the Supermen)
Kryptonian artifacts would also play a part in the Superman mythos. Devices such as the Eradicator would clone Superman and try to impose a more rigid Kryptonian dogma on Earth during the Death of Superman Saga.
Finally, there were other descendants of Kryptonians in the DC Universe. The agricultural world of Daxam was filled with former Kryptonians who had left generations before the destruction of Krypton. Daxam orbits a red star, so the Daxamites have no powers there.
Due to genetic instabilities, they are highly vulnerable to lead and need scientific intervention if they are to leave their world. Daxamites can become super-powered under a yellow sun or blue sun. Their current iteration in the DC Universe has left their civilization decimated after several occupations by other alien species.
Superman's history is very long and has been through a number of rewrites, continuity changes, complete universal reboots and contingent parallel realities. Sometimes he is truly the Last Son of Krypton (See: Red Son, and The Nail) and in some of them he is the head of an entire pantheon of godlike beings. (See: DC: One Million)
