The first Superboy that Superman met was actually from an alternate Earth known as Earth Prime. That Superboy had been sent from his universe's Krypton as well. Their similarity ended there, however; that Superboy hadn't had the Kents to raise him, and was in fact his Earth's only superhero. Sadly, his Earth was destroyed during a great Crisis, along with countless other versions of Earth. Superboy went off into limbo at the end of that Crisis, presumably never to be heard from again.
The next time Superman met a younger version of himself was before his journey to the
Pocket Universe. In fact, that Superboy was from the Pocket Universe, a universe created by the Time Trapper, a foe of
the 30th century's Legion of Super Heroes. Superman followed this Superboy into the Pocket Universe, where the truth behind
the Trapper's machinations was revealed. Superman returned to his Earth while Superboy and the Legion battled the Time
Trapper.
After Superman's death in his battle with Doomsday, the genetic researchers at Cadmus Labs created a clone which they
hoped would replace Superman. Created from the DNA of a human donor and using energy culled from Superman's own body-
generated protective aura, the clone would have been able to mimic most of Superman's powers and abilities, had it reached maturity in the
protected and monitored environment of Cadmus Labs. But the clone was released prematurely, before either his body or mind
had reached adulthood. This younger version called himself Superman and appeared on the scene at the same time as three
other individuals also claiming to be the Man of Steel, returned from the dead. But when the real Superman returned, the
young clone ceded the title and took to calling himself Superboy.
Superboy returned to Cadmus, albeit somewhat reluctantly. Under the guidance of the Guardian and some other friends at
the lab, Superboy explored the limits of his powers, particularly his "tactile telekenisis." Superman, impressed with the
growth and maturity the young clone was showing, gave him a Kryptonian name, Kon-El. This mark of respect from the Man of
Steel showed that the young Superboy was truly a part of the Superman Family.
When Superman was captured and brought to trial before the Tribunal, the Alpha Centurion recruited Superboy, Supergirl, Steel, and the Eradicator to try to rescue the Man of Steel. Superboy was suspicious of the Alpha Centurion, however, remembering the ease with which the Cyborg had deceived everyone. When the Cyborg was revealed to be the villain behind Superman's abduction, however, Superboy apologized to the Centurion.
Superboy teamed up with Robin and the young speedster known as Impulse, and created the group Young Justice--joined by a new Wonder Girl, an archer known as Arrowette, and other young heroes. The heroes of Young Justice had many adventures around the globe and even in deep space, always under the watchful eyes of their senior sponsors from the Justice League.
Eventually Young Justice was disbanded, and Superboy, Robin, Impulse (now calling himself Kid Flash), and Wonder Girl joined the Teen Titans. It was during his time in the Titans that Kon-El discovered the identity of the donor of his human DNA: Lex Luthor! Horrified by this revelation and its implications, Kon-El left the Titans and moved in with Jonathan and Martha Kent. Taking the name Conner Kent, he stayed in isolation in Kansas until a new global crisis emerged.
This new Crisis was brought on by the Superboy of Earth Prime, who had escaped from limbo and set about restructuring the universe. Enraged at what he felt was Conner's disrespect for the legacy of Superman, Earth-Prime Superboy attacked. The battle between the two Superboys was epic. Tragically, in that final confrontation, Connor Kent was killed.