The following games have been licensed by the Tolkien estate through Beam Software, even though it would appear that the estate does not own the rights to other kinds of games based on The Hobbit and The Lord of the Rings.
The following game has been licensed through the commercial company Tolkien Enterprises, which owns the rights to merchandising based on The Hobbit and The Lord of the Rings. The list includes games that have been licensed but not released.
These games have no official license at all. With the exception of the parodies, they could be regarded as violating copyright, but to my knowledge, legal action has not been taken against any of them.
Public Domain and Shareware games, as well as MUDs, are listed on separate pages, even though these do not have a license.