What makes the Greek myths in the Lightning Thief appeal to modern-day kids?

Are you kidding?  What modern-day kid isn't enthralled
with magic, magical creatures, flying without planes, abnormal strength, and other
equally cool stuff?!

Percy is just like most kids in my
class.  He is restless, diagnosed with ADD, and his mind wanders profusely.  He isn't
interested in school, doesn't like reading, but is intrigued by the stories of the Greek
gods.  When his teacher turns into some magical bird with huge wings and tries to attack
him, he is really focused.

He is intrigued by the stories
of gods having children with mortal women, and well he should be since he is actually
the son of Poseidon.  Of course, he's never met his real father, but he does have many
of his attributes, including, but not limited to, his love of
water.

There is also the story of the Sirens and their
ability to lure people in and trap them for years at a time with their lotus potions. 
Percy and his friends visit this place and are trapped for a short while during their
search for Zeus' lost lightning bolt.  However, once they realize they should stop
eating the lotus that flows freely at this outrageous party, they are once again
clear-headed and able to focus on the task at hand.

Percy
is also intrigued by the other children of gods and goddesses that he meets and trains
with at the camp.  There, he discovers that he does indeed have hidden powers and that
he is much stronger than he ever imagined.  The coolest thing he can do is heal himself
and others using water...a clear clue as to his parentage.  What modern boy wouldn't
want to be able to do that?

These stories are timeless and
universal.  It's obvious from all the TV shows about heros and people with special
powers that this sort of thing continues to amaze and captivate people of all
ages.