The Lord of the Rings, Volume 1: Fellowship of the Ring was released by Interplay sometime between 1983 and 1991. It is a turn-based RPG and only runs in DOS. If you're lucky, you can find this game on Interplay's 10th Anniversary anthology CD.
This game takes you from the Shire to an unorthodox ending at Dol Guldor. The game follows the general story line from the book, but many of the situations are not related to the books in any way. You can get about 10 characters to join your group, and up until Rivendell, most of these will be NPCs created by the developers, not appearing in the book. Many of the quests are the same way, but several of these tend to have some inspiration in the books at least and can be relatively fun, making every quest you can find worth doing.
Gameplay includes all the basic features of classic RPGs: stats, inventories, turn-based combat, etc. Characters in your group having knowledge of certain lore will reveal information about the areas you enter. You can talk to most of the NPCs. Some will give you text, and others with longer pieces of text will point you to the manual holding several such paragraphs of info. Don't think you can spoil the game by reading the manual though, because not all of them are even used in the game. The way NPCs will "react" to certain words is amusing as well.
This is an old game, so the sound effects and music aren't that great, when existing at all. It can only run in DOS mode, which means on some computers it will actually shut down windows to get to DOS. Processors are so fast that you can barely if at all see attack swings during battles. Getting around is a whole lot faster, though. There are some amusing and fun things to do though (try mining mithril in Moria), and the game doesn't end just because Frodo dies, so long as you can pass the Ring to someone else. For such an old game, it is fun to play.