The Guests ended up at Gregory House because they attempted/committed suicide.
- Here's what I think happened: The First Guest had realized early on how dull and boring his life was, and saw suicide as the only way out. So he tried to kill himself and wound up at the hotel in the first place—however, he wasn't actually dead, just comatose and in the hospital, so he still held onto his sanity and still wanted to leave and go home. Returning to reality was him waking from his coma, but he remembered why he'd attempted to kill himself in the first place. Some of the final shots in live-action are of a street and of a flashing light that appears to be a siren. Meaning the First Guest, on his way to or from work, stepped out in front of a car and died on his way to the hospital. The Second Guest was also Driven to Suicide due to her despair of her situation. I don't have any idea as to how she died, but she never woke up from her attempt, lingering until she finally kicked the bucket and remained in the hotel for all eternity. Some cultures/religions do believe suicide victims to be "lost souls" and believe they can go to neither Heaven nor Hell... This probably happened to the Guest in the PS2 game as well, considering that Gregory, when trying to convince you to stay, tells you to remember "that dark night," which is how the First Guest described the day he first entered the hotel.
- The purpose of the hotel seems to be to prevent people from returning to life. Dying in Gregory House doesn't necessarily equal death in the real world (see: the literal 'fire escape' at the end of Season 2). Gregory House is the equivalent of holding people down until it's too late for them to do anything. As Gregory says in Season 1, "Remember, he mustn't recover but he mustn't die."
One person managed to escape Gregory House and remember it a little; his experiences inspired a song.
As the third season and espescially its first episode reveal, people who fall prey to Gregory House aren't necessarily bound to it and are merely the prisoner of the soul-hungry Gregory Mama, but they are forever trapped in the world in which it exists. Look at poor Stephen Haniwa. You can check out any time you like, but you can never leave. He ended up 'checking out' in a different way after he managed to return to life, too.
But, as Gregory would say, why would you ever want to leave? Such a lovely place... such a lovely place...
Gregory is a prisoner of the hotel as much as the other guests.
- Gregory is the manager of the hotel, and it's implied to be something more than an old, smelly rat. He understands what the guests are afraid of really quickly, and will use it to his advantage to psychologically beat them into surrender. Plus, while many other guests are so fixed with their little obsession, he seems much more calm and rational. But he is not immune to what the hotel has to offer: he fell into Catherine's "cures", for instance. Then comes his "family": James, his troublemaker grandson who gives him more than one headache, and his really unbearable mother. And then there is Neko Zombie. Gregory apparently physically tortured him, and he never did something that directly threatening to anybody else; Neko, while holding a grudge against Gregory, apparently doesn't have this as obsession, i.e. his hate against the rat is not the reason he is stuck in the Hell Hotel in the first place. Plus, Neko Zombie is one of the few characters to seriously threaten Gregory - he even burned down the hotel! I think that, while Gregory is in charge of the hotel/purgatory, he is still affected by it. Therefore, since the Hotel works on the fears and obsessions of his guests, sometime it arranges things so that Gregory's fears became true. In particular, two of them are especially strong and destructive: the destruction of the hotel, his "playground", and Neko Zombie freeing himself and chasing him down.
Gregory is a True Fae (Gregory Mama might also be), and everyone else is a changeling.
The First Guest owned one of the first modern mobile phones.
He died in 1976, and to prevent anyone else from acquiring the model he was testing, Motorola let his family bury him with it. It took on a different form in Gregory's world, but retained some of its chunkiness. Who says you can't take it with you?