I'm looking to add to the list below:
Harry Potter_//_Lord of the Rings.
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Dementors_//_Nazgul.
Deatheaters_//_Orcs.
Haggrid_//_Beorn.
Hog's Head_//_Prancing Pony.
Invisibility cloak_//_Invisibility ring.
Horcruxes_//_The rings of Men & Dwarves.
Ring horcrux_//_The One Ring.
Butterbeer is served at the tavern_//_Butterbur serves the tavern.
Dumbledore_//_Gandalf.
Gryffindor's sword_//_Sting & Anduril.
Voldemort_//_Saruman & Sauron.
Dursleys_//_Sackville-Bagginses.
Bowtruckles_//_Ents.
Sirius Black_//_Aragorn & Boromir.
Pensive, Erised mirror_//_Galadriel's mirror.
House Elves_//_Tolkein-style Goblins (Physical appearance).
Rowling-style Goblins_//_Dwarves (Smithing, weaponcraft, infatuation with gems & shiny metals).
Ron Weasley_//_Samwise Gamgee.
Kreacher & Dobby_//_Smeagol (Gollum).
Harry's murdered parents_//_Frodo's drowned parents.
Harry lives with uncle_//_Frodo lives with uncle.
Forbidden Forest_//_Old Forest, Mirkwood, Fangorn.
Wormtail_//_Wormtongue.
Aragog_//_Shelob.
Werewolf army_//_Wargs.
Womping Willow_//_Old Man Willow.
Harry's wandmade scar_//_Frodo's Morgul Blade scar.
Harry's permanent head scar-//_Merry's permanent head scar.
Parseltongue_//_Blackspeech.
Don't say Voldemort_//_Don't say Mordor.
Skull & snake_//_Eye of Sauron.
Harry's telepathic dreams of Voldemort_//_Sauron's connection to the ring & the Morgal scar bearer's ability to sense Nazgul.
Hippogryff rescues Sirius from Hogworts tower_//_Giant eagle rescues Gandalf from Orthanc tower.
Harry Potter_//_Lord of the Rings.
--------------------------------------…
Dementors_//_Nazgul.
Deatheaters_//_Orcs.
Haggrid_//_Beorn.
Hog's Head_//_Prancing Pony.
Invisibility cloak_//_Invisibility ring.
Horcruxes_//_The rings of Men & Dwarves.
Ring horcrux_//_The One Ring.
Butterbeer is served at the tavern_//_Butterbur serves the tavern.
Dumbledore_//_Gandalf.
Gryffindor's sword_//_Sting & Anduril.
Voldemort_//_Saruman & Sauron.
Dursleys_//_Sackville-Bagginses.
Bowtruckles_//_Ents.
Sirius Black_//_Aragorn & Boromir.
Pensive, Erised mirror_//_Galadriel's mirror.
House Elves_//_Tolkein-style Goblins (Physical appearance).
Rowling-style Goblins_//_Dwarves (Smithing, weaponcraft, infatuation with gems & shiny metals).
Ron Weasley_//_Samwise Gamgee.
Kreacher & Dobby_//_Smeagol (Gollum).
Harry's murdered parents_//_Frodo's drowned parents.
Harry lives with uncle_//_Frodo lives with uncle.
Forbidden Forest_//_Old Forest, Mirkwood, Fangorn.
Wormtail_//_Wormtongue.
Aragog_//_Shelob.
Werewolf army_//_Wargs.
Womping Willow_//_Old Man Willow.
Harry's wandmade scar_//_Frodo's Morgul Blade scar.
Harry's permanent head scar-//_Merry's permanent head scar.
Parseltongue_//_Blackspeech.
Don't say Voldemort_//_Don't say Mordor.
Skull & snake_//_Eye of Sauron.
Harry's telepathic dreams of Voldemort_//_Sauron's connection to the ring & the Morgal scar bearer's ability to sense Nazgul.
Hippogryff rescues Sirius from Hogworts tower_//_Giant eagle rescues Gandalf from Orthanc tower.