Salvation

Boat — The survivors spot a sailboat, and ask a simple question: "saved?" ("Live Together, Die Alone, Part 1")

Being physically rescued or saved from the Island was the original goal of the survivors. As the story has progressed, some characters seem to have become complacent or accepting of the situation and focus less on the goal of being saved.

Occurrences

The following list shows when characters have mentioned, sought, avoided or received salvation from the Island.

Season 1

Boone checked the signal on his cell phone shortly after the crash. ("Pilot, Part 1")
Sayid recruited Charlie to help build a signal fire shortly after the crash. ("Pilot, Part 1")
On the first night after the crash, Sayid told Charlie that he thought someone would've come by now. ("Pilot, Part 1")
Boone offered a candy bar to Shannon, saying that they might be there for a while. Shannon refused, saying that the plane had a black box, and that she would eat on the rescue boat. ("Pilot, Part 1")
Jack and Kate decided to search for the cockpit in order to retrieve the transceiver and send out a distress call. ("Pilot, Part 1")
The pilot told Jack and Kate that the plane was 1,000 miles off course when it crashed and that the rescue team was looking in the wrong place. ("Pilot, Part 1")
After having acquired the transceiver, Jack tried and was unable to get a signal. ("Pilot, Part 2")
Shannon refused to help Boone sort clothes, saying "You're wasting your time. They're coming." ("Pilot, Part 2")
Sayid volunteered to fix the transceiver in order to make a distress call. ("Pilot, Part 2")
Michael told Walt that when they got home, he would get him another dog. ("Pilot, Part 2")
Sayid, Kate, Sawyer, Charlie, Shannon, and Boone hiked to higher elevation to send a distress signal. ("Pilot, Part 2")
Hurley tested to see if Mars was unconscious by yelling, "Yo, there's a rescue plane! We're saved! ("Pilot, Part 2")
Upon first hearing the French distress signal, Charlie was convinced it would be the rescue party. ("Pilot, Part 2")
Sayid told Charlie that satellites wouldn't help anybody find them if they didn't know where to look. ("Tabula Rasa")
Jack decided to burn the bodies in the fuselage, acknowledging that the rescue team was looking in the wrong place. However, Kate told Charlie that he delayed the fire until sundown in case anyone would see it. ("Walkabout")
Wanting to help Sayid triangulate the French transmission, Sayid told Kate, "It appears you are as anxious to get off this island as I am." ("Walkabout")
Sun told Jin, "I don't think anyone is coming." Jin replied, "Someone will come." ("White Rabbit")
Boone asked Jack, "Who appointed you our savior, huh?" ("White Rabbit")
Claire asked Charlie when they will be rescued. Charlie replied, "Soon." ("White Rabbit")
Locke told Jack that the other survivors were waiting to be rescued. ("White Rabbit")
In his "live together, die alone" speech, Jack told the other survivors that they need to stop waiting to be rescued. ("White Rabbit")
Jack told Kate that the survivors who were still waiting for a rescue boat ought to think about their safety. ("House of the Rising Sun")
Sayid told Jack that their best hope for survival was to build a signal fire to be rescued. ("House of the Rising Sun")
Michael didn't want to move to the caves, as that might have meant missing a rescue boat. ("House of the Rising Sun")
Sawyer framed the question as to whether or not to move to the caves as either "going with the pessimists, or staying here and waiting for the rescue boats". ("House of the Rising Sun")
Kate told Jack that she didn't want to move to the caves and "set up house" on the Island. ("The Moth")
Sayid devised a plan to triangulate the source of the French distress signal. ("The Moth")
Locke sabotaged Sayid's plan to locate the source of the French distress signal. ("The Moth")
Claire told Charlie that she wanted to stay on the beach for when they get rescued. ("Confidence Man")
Sayid asked Rousseau to come back to the camp with him, saying, "the only way out of this, this place, is with their help." ("Solitary")
Jack said of Kate sinking into the sand, "You're going to just sink your way right off the island. Sayid would be proud." ("Raised by Another")
Walt burnt the first raft because he didn't want to leave the Island. ("...In Translation")

Season 2

When asked to explain his history on the island, Desmond tells Jack about Kelvin, who told him that pushing the button was for "saving the world". ("Orientation") ("Live Together, Die Alone, Part 1")
After waking up from a delirium, Sawyer asked Kate: "Are we saved?" ("What Kate Did")
Charlie sang "All alone, I try to be invincible/Together now, we can be saved." ("Fire + Water")
Charlie's mother, upon giving him a piano, declares that he will "save them". ("Fire + Water")
Bernard tries to build an S.O.S. sign, and says "Everybody on this island is building something. I'm trying to get us saved." Mr. Eko replies "People are saved in different ways, Bernard." ("S.O.S.")

SOS sign made by Bernard in "SOS"
Rose and Bernard decided they didn't want to leave the Island because it healed Rose's cancer. ("S.O.S.")
The survivors see the Elizabeth, and ask if they are "saved". ("Live Together, Die Alone, Part 1")

Season 3

The lyrics that Charlie sing of the Oasis song Wonderwall are: "Because maybe, you're gonna be the one who saves me..." Later on, Desmond tells him that he has been trying to save his life repeatedly, first from being struck by lightning, and later by drowning. Desmond thinks that he may not be able to prevent Charlie's death, no matter what he does. ("Flashes Before Your Eyes")
Claire thinks she can get everyone off the Island by attaching a message to a tagged seagull before it migrates. ("Par Avion")
Locke blows up first the Flame communication station, then the submarine and later tries to stop Jack from making the call on the Satellite phone to the freighter. He seems determined not to let anyone get off the Island. ("Enter 77"), ("The Man from Tallahassee"), ("Through the Looking Glass, Part 2")
Naomi tells Hurley that the Oceanic Flight 815 has been found and there were no survivors, so no one could be saved. ("D.O.C.")
Desmond had a flash of the future, in which he saw Claire and Aaron leave the Island via a helicopter. ("Greatest Hits")

Season 4

With the freighters arriving via helicopter rescue seems close at hand. ("The Beginning of the End")
Daniel Faraday states: "I'm here to rescue you." ("Confirmed Dead")
Sayid and Desmond leave for the freighter on the helicopter. ("The Economist")

Flashforwards

Jack Shephard is seen off the island, along with Kate. ("Through the Looking Glass, Part 1")
Hurley Reyes is shown to have made it off the island. ("The Beginning of the End")
Sayid Jarrah gets off the island in the future. ("The Economist")
Aaron Littleton is seen to have made it off the island, in the care of Kate. ("Eggtown")
Sun Kwon is seen to have gotten off the island. ("Ji Yeon")
Walt Lloyd is seen off the island. ("Meet Kevin Johnson")

The Others

Some of The Others are able to leave and return to the Island. In Miami, Florida, Ethan and Richard recruited Juliet to come work on the Island. ("Not in Portland") ("One of Us") On the day of the crash of Flight 815, Richard was apparently in Miami, where he was filming Juliet's sister and nephew in a public park. ("One of Us") It is implied that Ben also leaves the Island, as Sayid discovered a secret closet in his house at the barracks containing multiple passports, cash in various currencies, and shoes and clothing suitable for the outside world. At some point in the future after survivors have made it off the Island, Ben is in Berlin, recruiting Sayid as a hitman. ("The Economist")