It used to be that a person who committed suicide was buried in a separate part of the cemetery and the relatives did not sit shiva (see Shulchan Aruch YD 345). We no longer do these things and we treat a suicide as a regular death. On what basis is this done?
First of all, I am not aware of any actual halachic source that states that a suicide is to be buried separately from the main Jewish cemetery. If anyone knows of a source for this, please let me know.
In any event, while many of the halachos of mourning do not apply in the case of suicide (Shulchan Aruch, Yoreh Deah 345), this is only true if the person committed suicide in a psychologically stable state of mind. In the absence of strong evidence to the contrary, the assumption of the poskim is that a suicide was not psychologically stable (see Aruch HaShulchan there).
This might sound as if it was effectively nullifying the law, because of course no one commits suicide when they are in a psychologically stable state of mind. However, while that is basically true of our own society, there have been many societies in the past where suicide was considered an "honorable" act under certain circumstances (e.g. the samurai practice of seppuku). While the assumption that suicide is the result of a state of instability is valid in our culture, it would not necessarily be valid in others.