First there was Middle-earth Role Play (MERP) from Iron Crown Enterprises. Then Decipher publushed The Lord of the Rings Roleplaying Game. Most recently there has been The One Ring Roleplaying Game published by Sophisticated Games partnered with Cubicle 7, followed by their Adventures in Middle-earth for D&D 5E.
CUbicle 7 has lost the rights for the Middle-earth games, but Sophisticated Games has now partnered with Free League Publishing (Fria Ligan) for a new edition of The One Ring and probably the D&D 5E setting as well. The first new release will probably be seen later this year or early in 2021.
I know of Lord of the Rings by ICE (if i'm not mistaken…. MERP by ICE and Lord of the Rings by GW... but there are bound to have been more…. :/
I forgot about that one. The LOR Adventure Game is a lot simpler than MERP. If you've ever played the Tolkien Quest game books, you'll already be familiar with the mechanics.
Soon after the movies came out Decipher produced a Lord of the Rings rpg. In recent years, Cubicle 7 produced The One Ring and Adventures in Middle Earth (D&D 5E is needed to play this). Cubicle 7 announced they will cease production of these games; another company may support them.
Let's not forget the other rpgs that were used to game in Middle-earth, even if the systems were not made specifically for Middle-earth. I've seen lots of versions of D&D in all its editions (I've done a few versions myself), GURPS, and HERO Systerm (I was doing a conversion from MERP, but I lost my notes). Someone on a different forum suggested that Burning Wheel would be a great system for gaming in Middle-earth.
In addition to the RPGs I listed, there have been almost countless board games and war games set in Tolkien's Middle-earth as well as card games (both collectible and non-collectible). Cubicle 7 also published the storytelling card game Hobbit Tales from the Green Dragon Inn. And it wasn't too long ago that Fantasy Flight brought out the co-operative board game The Lord of the Rings: Journeys in Middle-earth.
Here's a list of house rules I came up for MERP, if anyone is interested: