The Elder Scrolls does this perfectly because it's intended from the start and doesn't commit what I see as cardinal sins.

The Cardinal Sins

Don't take a character and change their personality.
See: Cloud. Don't take a guy with large, steely determined eyes and packed with muscle in your original game (just look at the game manual's character pages) and turn him into an afraid, skinny, emo pansy.

If they had no voice, leave it that way.
Different people will have different thoughts on how a character talks, and when you give them a voice, it screws up that impression and leaves them not liking the change. Again, Cloud commits this sin.

Don't use time travel.
XIII suffers from this. As soon as you put time travel into a game, it basically puts in too many loopholes. Things won't make enough sense.

Plan it from the start.
Don't create a game that is fantastic, amazing, and complete... and then say "Wow, that went better than we thought. Let's make a prequel/sequel." See: VII.

Let everyone know it from the start.
If you do have a sequel planned, don't pull an XIII-2 and have the ending go "BUT WAIT, THERE'S MORE!" The ending may as well have been a Rick Roll.

Don't rewrite the original game.
We all saw the ending of XIII, and when XIII-2 started, it just crapped all over it.