This comes from personal experience, and it depends on what you would like to have happen.
If you want to have the leaving character potentially come back:
- that character is going on a side quest. Something personal takes up that character's time, and they want to do it on their own. This justifies the character coming back and being at a similar experience level as the player characters who didn't leave.
- that character has decided that there are easier ways to make a living; they go into "adventurer retirement," and use their wealth from adventuring to live a normal life. Assuming you want your PCs to be about the same level all the time, you will have trouble obtaining a justifiable reason for a change in the character's level if they do come back from "adventurer retirement." The tolerance for this varies within groups; some are OK with everyone being the same level, others want individual experience to be tracked.
If you don't want the character to come back (make sure the leaving player is OK with this, or social bad times can happen):
- Kill off that character. Adventuring ought to be a dangerous business.
- Turn them into a villain! This makes for a much more personal villain.
These four solutions have worked well with past groups I have been in. As always, you don't want to offend the people with whom you play, otherwise you may find yourself without people to play an RPG with.