In The Great Gatsby by Fitzgerald, does Gatsby ever achieve his American dream? What evidence from the text supports this?

Gatsby never does achieve his American dream.  For him, the dream wasn't just about getting rich, which he's already done.  The wealth was just a means to an end; he wanted to get rich so that he could win back Daisy.  He knew that she could never be with him if he were not wealthy, and so he must acquire wealth before he can acquire her.  Gatsby would stare and stare across the bay at the green light at the end of Daisy's dock (this is what he's doing the first time Nick sees him), and it came to be a symbol of her, of his dream of her.  In the end of the novel, he waits and waits and waits for her call, the call that would tell him that she chose him, that she was leaving Tom for good.  He said to Nick, "'I supposed Daisy'll call [...].'  He looked at [Nick] anxiously, as if he hoped [Nick would] corroborate this."  But she never does.  Finding out how Gatsby had acquired his wealth -- illegally, as a bootlegger -- was enough to scare her away from him forever.  And since she was the dream, never being secure of her meant that Gatsby never achieved his dream.