Yes yes yes I know technically he is not a Padawan...and yet he is.
Although never called "Padawan" there was the same relationship,
however brief, with Obi-Wan as any other Padawan learner might have.
Besides, Lucas probably hadn't thought up the term at that point.
So I am including Luke because in my opinion he was a legitimate Padawan.

When Luke Skywalker was just a baby, he was brought by Obi-Wan Kenobi
to live with Owen Lars. Luke lived with the Lars' on their farm located on
Tatooine. When he was around twenty, the Lars' bought two droids
(C3PO & R2D2). R2D2 ran away, and Luke had to go after him with C3PO.
R2D2 apparently had the plans for an Imperial space station called the Death Star.
Princess Leia, a rebel (actually Luke's sister), had placed the plans in R2D2 and
when her ship was attacked had sent them down to the planet for Obi-Wan Kenobi.
Luke was attacked by Tuskan raiders and rescued by Ben Kenobi (Obi-Wan).

Ben Kenobi asked Luke to come with him to Alderaan to see the droids delivered
to Leia's "father" Bail Organa. Luke refused saying he needed to stay and help
Owen Lars, but when he got home he found that some imperial troops (after R2D2)
had burned his home and the Lars'. He returned to Ben Kenobi and agreed to
come with him to Alderaan. "There's nothing for me here now. I want to learn
the ways of the Force and become a jedi like my father." The two of them (along
with the droids) arrived at Mos Eisley spaceport. There, in the cantina, they met
Han Solo and Chewbacca who agreed to take them to Alderaan...for a price.

When on the Millenium Falcon (Han Solo's ship), Ben began teaching Luke
some basic jedi training. But when they finally reached Alderaan, they found
that it had been blown away. They were caught in a tractor beam by the Death
Star, and pulled into one of its gigantic hangers. Through some sneaking around,
they managed to get away from the ship and try to figure out what to do. Ben
suggested that he could turn off the tracter beam,and then they could leave safely.

When he left, however, Luke found that Princess Leia was being held prisoner on
the Death Star. He persuaded Han Solo to help him rescue her. After many adventures,
the now four of them got to the hangar where the ship was only to find Ben Kenobi
and Darth Vader (really Luke's Father) in a deadly lightsabre duel. Luke watched as
Obi-Wan Kenobi was killed, but he left with the rest anyway. He even managed to
blow up the Death Star and save the rebellian against the Empire. Later, on Hoth
(the new rebel base), Obi-Wan appeared to him and said to go to the Dagoba system
to be trained by Yoda. Luke did, and learned much from Yoda, including how to see
the future. What he saw was Leia and Han in dreadful pain. Horrified, he rushed off to try
and rescue them. Indeed, Leia and Han had been captured and were in pain.
Han was frozen in carbonite by Darth Vader just before Luke arrived. In a battle with
Darth Vader, Vader informed Luke that he was his father. Luke got away, and went with
Leia back to the rebels.

Through a group effort, Leia and Luke rescued Han from Jabba the Hutt and
unfroze him from the carbonite. Luke returned to Master Yoda, only to find him
dying. Yoda told Luke "You must confront Vader. Then, only then, a jedi
will you be." Yoda confirmed that Vader was Luke's father and Obi-Wan informed him
that Leia is his sister.The rebel alliance came up with a plan that would destroy the
new Death Star II and the Emperor, which Leia, Luke and Han were to participate in.
They had to take out the shield generator that protected the Death Star II, while
fighters flew into the Death star and blew up the main reactor. Darth Vader, sensed
Luke's presense. Luke, to save the mission, gave himself up to Vader and was taken
up to the Death Star II. The Emperor tricked him into fighting Vader and Luke
accidentally betrayed that Leia was his sister. Vader, who in truth cared for Luke, did
not use the Dark Side to fight as was his wont, but weakened as he did not wish to
kill Luke. Luke, in a fit of rage, nearly killed Vader.

When the emperor called for Luke to join the Dark Side, he refused. The emperor used
the Dark Force Lightning in an attempt to kill Luke. Luke in his agony called on his father.
Finally, Vader could stand no more and flung the Emperor into the shaft down to the
powercore. But the effort was too much for him and he died in Luke's arms, having
turned once again to the Light Side. Luke became a jedi and went on to teach others
(including Leia) to use the Force. The rebel alliance slowly gained control and
Luke started a Jedi Acadamy.

Obi-Wan : Anakin : Luke : Humour : Allies : Contact