The ending of Shutter Island seems ambiguous to many people, but again, to me it was pretty clear-cut. Teddy wakes up to the reality that he is actually Andrew Laeddis, though he is warned by Dr. Cawley and Dr. Sheehan that he has regressed into his fantasy world before. However, Andrew is smart: When Dr. Sheehan sits with him on the steps that next morning, Andrew knows that the doctors and Warden are observing his behavior. The thing is, his guilt and pain are still so heavy that he knows he cannot live with them;  rather than live with the knowledge of his pain, he chooses to pretend that he is still Teddy Daniels and let them lobotomize him, so that he can finally be free of his burden.Thats what the line to Dr. Sheehan about living as a monster, or dying as a good man, means - Andrew would rather be mind-wiped as Teddy Daniels than live with the sins of Andrew Laeddis. The End. 
DEBUNKING THE CONSPIRACY THEORIES
I teach classes on literature and literary analysis and one of the hardest techniques to teach students is how to accurately analyze a text, based on what is on the page. People read into things all kinds of ways - but you should have concrete evidence from the source material to back those theories.
Here is a list of some things that people who believe Shutter Island was an evil government lab, or that Teddy Daniels was sane and got tricked in the end, should keep in mind:

When the film opens, Teddy is on a boat headed for Shutter Island (the boat is real, by the way). The room Teddy is in has manacles and shackles hanging in it - restraints for the prisoners being brought to the island, and likely where Teddy/Andrew was held before the role play experiment began. As for when Teddy resets his memory? Ill admit its a bit of a plot hole.

In the lighthouse, Dr. Cawley tells Andrew that he is seeing things and feeling body tremors because of withdraw. No, the cigarettes and pills Teddy takes throughout the movie are not meant to drug him - in fact its the opposite. Cawley and Sheehan take Andrew off his meds for the role play experiment, in order to help him break through to reality. As the film goes on, Teddy begins to have more vivid hallucinations while hes awake - his meds were meant to suppress that type of psychosis, not inspire it. Going off the meds is what makes him go so nuts later in the film.

Fire is a symbol of Andrew/Teddys insanity in the movie. If you watch closely, every time Teddy is around fire - the matches he lights in Ward C, the fire in the cave with Dr. Solando and when he blows up Dr. Cawleys car near the end - he suffers some sort of hallucination. Fire is the symbol of Andrews fantasy world, while water (the opposite of fire) is the symbol of the reality of what happened to him. His wife drowns his children in water and it is water which makes Andrew so upset/uneasy/sick throughout the film. So that cave scene with Dr. Solando? Yeah, she isnt real - and therefore her whole spiel about Shutter Island being a secret government mind control lab isnt real either.

The hurricane is real. Its just Boston weather and a cinematic throwback to old pulp Noir movies like Key Largo. Thats it.

Jackie Earle Haleys character, George Noyce, is a guy who knew Teddy/Andrew in the asylum. Noyce was a repeat offender who ended up back on Shutter Island and fed Andrew conspiracy theories for his fantasy. One day Noyce called Teddy by his real name, Laeddis, causing a psychotic outburst where Andrew beat him up. That assault is what caused Dr. Naehring and the Warden to push for Laeddis to be lobotomized, causing Dr. Cawley and Dr. Sheehan to create the role play game as a last-ditch effort to cure Laeddis.