While the answer is a matter of personal opinion, there are several Lord of the Rings games that are highly regarded. According to Metacritic, the highest-rated, standalone Lord of the Rings game is "The Lord of The Rings: Return of the King" for PlayStation 2 with 86 percent.
In addition to that game, there are many others with high ratings. Three expansion packs for the massively multiplayer game "Lord of the Rings Online" are very highly regarded, each with a score of over 85 percent. "The Lord of the Rings: Battle for Middle Earth" on PC is also rated highly, with a rating of 84 percent.