Though this question would be great to know for various legal systems, I'm tagging this with united-states since it will likely be complicated enough with just a single country being considered.
When can someone be legally required to enter a facility because of their mental illness? Are there particular diagnoses that would be enough? Would they have to commit a crime first? Could a doctor require it of them?
The primary reason for involuntary commitment is that a person poses a threat to themselves or others.
This is usually intentionally broad, but can be taken to mean suicidal, delusional or homicidal tendencies, or other personality disorders that make a person a threat.
There are usually provisions for holding a person for a limited period of time in emergency situations - for example, if they have recently attempted to commit suicide.
Each State will have different standards required to have a person involuntarily committed beyond this emergency period. However, in general, if a person is a danger to themselves or others unable to provide for themselves, and will continue to be without assistance, then they will meet the criteria for involuntary commitment.
This chart has some elaborated and detailed information, state-by-state.
