1408/WMG

Mike didn't destroy whatever was haunting the room at the end of the movie; he set it free.
The bricks that appear to seal off the room have 'burn me alive' carved into them, which the movie makes a point of having him notice twice. He thought that he was heroically sacrificing himself to kill the evil force by destroying the room, but it actually put the idea into his head on purpose because once the room is destroyed (or rather, destroyed by something "real" instead of its own powers; as Mike said "fire is real") the ghost or whatever it is is no longer trapped within it and can go out in the world as it pleases. Its attempts to stop the fire by turning on the sprinklers were actually it goading him into making the fire larger by making him think it was working, since initially it wasn't strong enough to completely destroy the room.

Its earlier attempts to drench and freeze him were also working towards that goal, since he had no way to keep himself warm apart from making a fire. Which did work slightly, except that he only made a tiny one instead of a large blaze.

Expanding on that...

All the suicides through jumping out the window have been partially-successful possessions that went wrong at the last moment.
While it could be reasonably theorized that the people were just trying to escape the Groundhog Day Loop, it is also plausible that 1408 was riding along, trying to get out as well. The trouble was, it was unable to fully take control to force them to do what it wanted, but it could use its talent for the Mind Screw to make them more receptive to possession. What it needed afterwards was not somebody trying to escape (as its express check-out system is necessarily fatal), but somebody leaving involuntarily, or at least not under their own power.

The entity in the room has possessed Mike.
Once released from the burning room, the entity had to hide somewhere to recoup its strength, as the process of losing its previous home for the past 54 years took a lot out of it. So it entered the handiest new host - Mike. It knew that once the fire alarm was set off, people would be evacuated, and once Mrs. Enslin arrived (brought by its hijacked video chat instructions) she would make sure the rescue team knew Mike was up there. Mike laughing like a maniac in the burning room was the sound of all the entity's plans coming together like a well-oiled machine.

The point where it makes itself known to the audience is at the very end, when the interference that was distorting the salvaged tape recorder suddenly goes away, and we hear the sound of their dead daughter, clear as a bell, on the tape. Either it voluntarily removed the distorting effect, or else it manifested that remembered voice in the device.

1408 allowed Mike to take away that recording of his dead daughter's voice as a reward for being the first to escape its clutches.
... turning the room into the Genius Loci equivalent of Jigsaw.

1408 works exactly the same as Silent Hill.
Only 1408 is its more subtle, smart cousin. Or, alternatively, 1408 is a Silent Hill town in a larval stage. It feeds off of death and/or tragedy. Silent Hill has had more victims, hence the size. The only reason 1408 hasn't expanded at a wildfire rate is thanks to the efforts of the hotel's manager, who makes sure it never gets a surplus of agony or death that it'd require to grow.
 * Or if we accept the notion of parallel universes existing, 1408 is this universe's equivalent to Silent Hill, or how the town manifests in that universe.

1408 is somehow related to IT
Both are experts in the arts of Mind Screw and Mind Rape, both use their victim's primal fears and insecurities against them, and both seem to be able to warp reality around them to their existence. 1408 was, unlike It, somehow trapped in that one location.

The true form of 1408 is that thing in the vents.
It'd work well with the last theory. Besides, when Mike begins to burn the room down, the thing in the vents is the one to yell at him. Why doesn't the room use an illusion, the TV, or even the radio? Simple, because the room wanted to say it itself.

All the people who have died in 1408 are still trapped there.
Consider Mike's visions (hallucinations?) of the previous victims. Each of these is a victim who decided to take advantage of the room's "express checkout"... and is now trapped in the room, reliving their hour of hell over and over again. How many times has that one woman thrown herself out the window? How many times has the sewing machine salesman slashed open his throat? How many times has that one victim drowned in his chicken soup?

The room is a thinny.
You enter the room and find an evil entity on the other side of the door. This makes sense if it's a small thinny that takes you to a place where everything is malevolent. Perhaps a guest bedroom in Le Casse Roi Russe?

Mike was in no physical danger at all.
Everything that happened in the room was an illusion, created from his darkest fears and regrets, so everything that goes on during his stay is in his own mind. The wound he gets from the window could be explained away as just a wiggy window sash, but notice how quickly everything else is "reset" once the countdown is over. That said, though, being dragged kicking and screaming through one's own personal hell, illusion or not, did put him in quite a lot of psychological danger...

1408 is an Eldritch Abomination.
... or at least a part of one that feeds on fear and anguish and any other negative emotion you can think of. Imagine an impossibly huge creature, living just under the surface of what we recognize as reality. It has a number of tendrils, each ending in a mouth of sorts, which it extends to the surface (our world, for those of you keeping score) to feed - not necessarily on meat, though this is often a nice bonus - but on emotions, which it needs to survive. Each mouth is not really an orifice as we might recognize it, but it takes the shape of something we might find comfortable and familiar, like an ordinary hotel room. Like many species of ambush predators, this functions as a lure to get its prey inside, and once the trap is sprung, it begins to feed, injecting a number of illusory tortures into the mind of its prey in order to get what it needs to survive. Destroying 1408 only cripped one such mouth, and it has more...

If someone who was completely satisfied with their life tried to stay in 1408...

 * Possibility 1: They would have a pleasant stay in a perfectly ordinary hotel room, because 1408 has nothing to feed on.
 * Possibility 2: There would be a blank wall behind the door. 1408 simply isn't interested in this prey.
 * Possibility 3: There would be an empty black void behind the door. No fears or regrets, no manifestation.
 * Possibility 4: It would ultimately kill 1408.

Building on the above...

The only certain way to kill 1408
Have an experienced Buddhist monk stay the night there and contemplate Mu all night.

The room wanted to be killed
It showed Mike "burn me alive," which given its general reality warping properties, it did not have to do. All the people it's killed, it was trying to make them fight back but they were all too weak. The room was in as much pain and misery as the people in it, and now it's at peace.
 * Now that we have a trope for this, it's the location version of Tortured Abomination.

The room itself sent the postcard.
Both endings show that the room can manifest some of its power outside itself. If this is the case, it could also prevent itself from being covered up or shut down, or could just move somewhere else. Since when were you under the impression there were any limitations on its powers?

Movie!Mike was having a crisis of faith after Katie died.
I know Mike was an atheist when everything started, but bear with me. Mike didn't believe in God or any sort of afterlife, which made Katie's illness and death doubly hard on him. He turned to investigating haunted sightings in the hopes of gaining proof - any sort of proof - that there was some form of existence after death, so he could rest assured that Katie Enslin didn't simply cease to exist when she died. His sensible mind simply wouldn't allow him to take things on faith, but despite the stories he was told, he saw no proof that there was an afterlife. In the middle of all the hell 1408 put him through, he did finally see proof of the paranormal, therefore proof of an afterlife, and therefore was reassured that the flame that was Katie Enslin lived on somewhere.

That was his daughter the room brought back.
The room has brought shades and ghosts of people who have died in it, in addition to recreating or duplicating many people. How do we know it didn't just bring her back to torture him?

1408 is an insane TARDIS!
It's been established that TARDISes are alive and have personalities. It wouldn't be much a stretch to say some could go mad and homicidal. Perhaps it was a survivor from the The Last Great Time War. Maybe it lost its Time Lord. Maybe it killed its Time Lord. Makes me wonder what that thing in the vents really is...
 * Maybe the thing in the vents is its Time Lord...