Fellowship of the Ring -- Of all the Lord of the Rings games, this is the one for everyone to skip. Allegedly there are scenes and characters included in the game that aren't in the movie, but you'll be lucky to make it far enough to find them. Unattractive, awkward and needlessly impossible to play.
The Two Towers -- Hot-shot video game publishers Electronic Arts took over the franchise for the second movie, and the results are a marked improvement. The story has enough action, and a reasonable resemblance to the world of the film. It may be a little easy, and unpolished around the edges but it still feels right enough to count as a successful extension of the franchise.
Return of the King -- The best of the Lord of the Rings games. Building on the successful job they did with The Two Towers, EA Games packs in more footage from the final film (although it's all stuff you can see in one of the longer previews), and more time with the characters. Players get to switch among Gandalf, Aragorn and Frodo, effectively playing three entertaining games in one. The default level is easy enough for non-gamers, but regular players can up the challenge.
The Hobbit -- Just released to coincide with the final installment of Peter Jackson's film trilogy, this game takes you back to the prequel to the Lord of the Rings. You play Bilbo Baggins as he travels with dwarves and Gandalf to fight Smaug, the dragon. Levels recreate chapters from the book; the storyline is engaging enough for kids and the gameplay is not overly complicated either. There are puzzles to solve and little missions to accomplish. Bilbo is a lot tougher here than you might have imagined him, and you get to guide him as he finds Sting and meets Gollum (keeper of the you-know-what). Like the book, The Hobbit offers a charming trip through Middle-earth.
War of the Rings -- Real-time strategy games are all about building an army and conquering your opponents before they can attack you. They're usually a good mix of patient strategizing and fast battlefield commanding. Unfortunately, while War of the Rings does have a good selection of units from the movies and books, the computer opponent puts up no challenge. Wait a few months for The Battle for Middle-earth, which is a similar game made by a company with a better track record.