Instructions
Three Methods to Remove Characters
Hold down "control" and left-click the character to bring up an option to remove the character from the party.
Choose a "reform party option" from the character interface.
Talk to an NPC. You may be given an option to invite him into your group. If your party is full, you will automatically get a "reform party" menu.
Anomen
Be careful with Anomen if your character is female and having a romantic relationship with him.
Help Anomen pass his test. If he fails, he will fight with Aerie or Keldorn.
Avoid making the wrong choices in the Saerk subplot during the Anomen romance; Anomen will leave the party and disappear permanently.
Incompatible NPCs
Do not mix incompatible NPCs, or some of them will leave permanently or be killed.
Do not have Minsc and Edwin in a party together; Minsc will kill Edwin.
Do not have Keldorn and Viconia in a party at the same time; Keldorn will kill Viconia.
Do not have Korgan and Aerie in a party at the same time; Korgan's insults will drive Aerie away permanently.
Male Character Romances
Do not remove female NPCs from your party if you are in the middle of a romance plot involving them.
Do not remove Jaheira from the party during the Jaheira romance. She will leave permanently and you will not be able to complete the Harper questline.
Do not remove Aerie from your party or make the wrong conversational choices during the Aerie romance or Aerie will leave the party and disappear from the game.
Alignments
Watch alignments carefully, because NPCs incompatible with your reputation will leave your party and become permanently unavailable in certain circumstances. If your reputation is 18 or above, evil characters will leave. If your reputation is 2 or below, good characters will leave.
Keep your charisma high. If you have extremely low charisma, NPCs of the opposite alignment may leave at 4 or 16. Use a "ring of human influence" to set your charisma to 18 to avoid this.
Pay attention to what NPCs say. NPCs will usually warn you if a conversation tree or alignment is close to triggering their leaving the party.