Forrest law is the son of Marshall Law, he made his first appearance in the king of iron fist tournament 3 taking his father's place, the reason why he took Marshall's place in Tekken 3 is unknown.    This would be the only cannon appearance by Forrest law,  as Namco didn't acknowledge him missing in Tekken 4.  It took Namco to get to Tekken 5 to acknowledge Forrest Law's Absence and to try to make it cannon, the story is that he got injured while riding around Paul Phoenix's bike.  Ever since that incident occurred, Marshall law has been trying to find a way to pay for Forrest law's injuries, so it's unknown if he'll come back as a playable character later on in the Tekken franchise.
Below is the list of games that Forrest law has appeared and been playable in:
Tekken 3
Tekken Tag Tournament.
Tekken Tag Tournament 2.
Forrest Law isn't a selectable character in Tekken 6, yet he has made an Easter egg appearance ; as he can be spotted in the Rustic Asia Stage.

Incase anyone's wondering about the Tekken 6 detail.
Someone on youtube by the name of: Linhgame uploaded a video proving this Easter Egg exists.

https://www.youtube.com/watch?v=28MukDf3PJM