There's the old LOTR games from 1986 and 1987, and the The Hobbit games. I don't see how The Hobbit was a spinoff, as the Lord of the Rings was was published 17 years after The Hobbit. And if I somehow misunderstood what you meant, what do you mean?
Games
http://en.wikipedia.org/wiki/The_Hobbit_(1982_video_game)
http://en.wikipedia.org/wiki/The_Hobbit_(2003_video_game)
http://en.wikipedia.org/wiki/Lord_of_the_Rings:_Game_One
http://en.wikipedia.org/wiki/Shadows_of_Mordor
Book Publication Dates References
http://en.wikipedia.org/wiki/The_Hobbit
http://en.wikipedia.org/wiki/The_Fellowship_of_the_Ring
EDIT:
stonerocker said:
People keep on bringing up LOTR. But no one has mentioned the original LOTR game for the snes, which came before the movie.
http://en.wikipedia.org/wiki/J.R.R._Tolkien%27s_The_Lord_of_the_Rings,_Vol._I
This must count.
EDIT: This game was released in 1990. But there was a cartoon movie based on lord of the rings released in 1978.
http://en.wikipedia.org/wiki/The_Lord_of_the_Rings_(1978_film)
which was followed by it's sequel title The Return of the King in 1980.
http://en.wikipedia.org/wiki/The_Return_of_the_King_(1980_film)
The Hobbit also had an animated film in 1977
http://en.wikipedia.org/wiki/The_Hobbit_(1977_film)
So do the games The Hobbit and The Lord of the Rings Vol. 1 count or not?
Well, I knew about the The Hobbit movie (yes, I know it came before the games), and I believe the games were based off the book. Who would want to base a game off of THAT movie?