What are some quotes that show the main characters in The Great Gatsby are trying to better their lives and achieve the American dream but fail?

Nearly all the main characters in Fitzgerald's
The Great Gatsby are trying to better their lives, which is, in
essence, trying to achieve the American dream.  Whether they achieve that goal or not
varies by degree, but in the broadest terms, none of them have much
success.

Jay Gatsby - achieves the American Dream in terms
of money, which is what the young Jay Gatz initially wants to do.  Once he falls in love
with Daisy, though, his dream changes and he wants only to be in a position to have her
love him.  In that he fails, as she doesn't love him enough to abandon her
life.

Tom and Daisy Buchanan - live the American Dream in
that they are careless people who get what they want and discard the rest.  Their
failure is a moral failure.

Jordan Baker - is living the
American dream of success in her chosen field.  Her success is tarnished, however,
because she cheats.

Myrtle Wilson - has a more modest
American Dream, as she simply wants to escape the life she chose and thinks money will
make her happy.  She did escape (until the end)  but she was even more unhappy when she
had to go back to her home.

George Wilson - has a very
modest American Dream, as he just wants more than he has.  His life is an abject
failure, as he achieves neither financial success nor personal
happiness. 

In short, virtually none of the main characters
in this novel achieve their version of the American Dream.