The One Ring (2nd Edition): Narrative-driven, character-focused, rules-light, collaborative storytelling—most critically acclaimed.
Middle-earth Role Playing (MERP): Rules-heavy (Rolemaster-based), tactical combat, deep character builds—classic 80s/90s feel.
Adventures in Middle-earth (5E): D&D 5th Edition ruleset, familiar mechanics, easy pickup for D&D players.
Lord of the Rings Adventure Game: Card/dice narrative system, lighter/casual.
Video Games (Single-Player)
The Lord of the Rings: The Fellowship of the Ring (PC, 2002): Classic RPG, dated but charming, follows book closely.
Middle-earth: Shadow of Mordor / Shadow of War: Action-adventure, Nemesis System creates unique enemy relationships—not traditional RPGs but deep progression.
LOTR Online: Free MMO (mentioned since you asked for alternatives)—vast world, story-focused.
Other
LOTR Card Game (LCG): Cooperative deckbuilding, iconic characters/locations.