You can see how to get to the endings and where your decisions will lead in this diagram.
I tried to keep the spoilers low, but the diagram is not completely spoiler-free.

See here what happens at the individual endings:

Ending 1:
You die in your cell by poisonous gas.

Ending 2:
The psychologist is a bit disappointed, but the warden congratulates you. You enter your cell alive.

Ending 3:
The psychologist and the warden argue. You keep walking through the facility a bit until you leave it alive.

Ending 4:
You enter a room that formerly had an exit. The psychologist is disappointed. You die in the room by poisonous gas.

Ending 5:
The choice button sinks into a pit. You die by flames.

Ending 6:
The choice button sinks into a pit. You die by spikes.

Ending 7:
You receive a new identity and leave the facility alive.

Ending 8:
The warden dies. You become the new warden and enter a surveillance room, alive.

Ending 9:
You receive a new identity. The psychologist congratulates you and you leave the facility alive.

Q: Some decision chambers have a time limit of one minute. What happens when the time runs out?
A: Usually you die by poisonous gas and the decision chamber starts again. "Start" and "The button" are notable exceptions.

Q: There is that test chamber within the easy levels. It has this big cage with a box in the middle, where you cannot enter the cage but move the box around. The warden says that I have five minutes for this test. What happens when the time runs out?
A: You die by poisonous gas and the test chamber starts again.

Q: What other impact do my decisions have?
A: Your decisions affect the order of the test chambers in the easy, medium and hard level blocks. They also affect the next few comments from the warden and the psychologist.

Q: Some choices claim to be "Fast", "Safe" or "Easy". What does that mean?
A: Nothing, it does not change anything. The resulting path does not become easier, safer or faster than other paths.

Q: So the choice system is a sham, my decisions barely matter and the endings are just waiting behind an Ending-Tron 3000?
A: Sort of.

Q: Can I just reload after an ending to see another ending?
A: No. Your savefile gets closed and you have to start a new game.

Q: Is there anything I can do about the savefiles?
A: The savefiles are located under SteamDirectory\userdata\SomeUserNumber\344410\remote\save. When you enter a decision chamber the game will autosave. Now open the directory and copy your savefile somewhere else. When you have seen your ending close the game, copy your savefile back and restart the game to reload from your branch point.

Q: Is it worth playing the game 7.5 times to see all nine endings?
A: No, I don't think so. It might be fun the first two or three times, but then it gets very dull. Fiddle with the save files or look for an ending compilation on Youtube.

Thanks to:
Captain Picard, for helping during the search for all the endings
Rapid, for finding the last ending