After I saw the category i thought about recommending and reviewing some videogames i played about Tolkien. Some games are hard to find as they were made by EA and they can't distribute them no longer. (perhaps EA and Warner could find a way to redistribute them but it won't happen) Also all are videogames as I haven't played a single tabletop game from the Lotr.
Lord of the Rings: The Return of the King
This is a hack and slash made by EA and it was released for the movie so doesnt say much about the story (but to be honest dont worry about that if you are here). It has single-player and co-op and it is best if you treat it as a party game as it isn't complex though it has some dificulty. It was distributed to PlayStation 2, Nintendo GameCube, Game Boy Advance, Microsoft Windows, Xbox, Mac OS.
Lord of the Rings: Battle for middle earth 2 : rise of the witch king
(realesed for PC and distributed by EA though some fans are remaking it)
This is a great RTS in the same style of age of empires and starcraft but intead of creating 1 guy at a time you create a whole batalion, the maps that come with it are good as you nor only have open battles but also sieges, though the IA is bad while being sieged, it also has some requiered balance with the expantion, the campaings are decent and the exantion one is good.
Fun fact: it has the record of longest title in videogames.
Middle-earth: Shadow of Mordor
I mean if you havent played it yet you are losing a marble (i havent played shadows of war as i need a better PC) An open world that death has consequences, as orcs that kill you become captains and fight with other captains to rise in the ranks of mordor, and not only that but the main story and the Bright Lord DLC are exelent. (I recommend complete the story and then play the DLCs as they have some spoilers)