Already been mentioned but the The Wizard of Earthsea (Earthsea Cycle) by Ursula K. Le Guin is the only other fantasy that feels "similar" to the Lord of the Rings to me (admittedly I haven't read a ton of fantasy, but I've read a decent amount). I'm reading through the series for the first time, on book three right now, and it's just great. Feel like it does a nice job of defying my expectations of a "fantasy story" and Le Guin's writing is beautiful.

Also these books straddle the line between fantasy and sci-fi, but the Broken Earth Series by N. K. Jemisin are amazing and among my favorite books. Actually gave the series a reread after my most recent reread of LotR earlier this year, so I can vouch they are an excellent follow up! These ones have less of an obvious fantasy parallel to LotR but they're too good for me to not mention!

The Shannara series by Terry Brooks has a reputation as being an homage to LotR, and they are quite enjoyable.

If you want to try and branch out and give Urban Fantasy (magic, but more modern society) a try there’s a reason that the Dresden Files by Jim Butcher are super popular. The book Dead Beat was written as a mid-series introduction for new readers to the series because Sci-Fi had just come out with a TV series and the 1st few books are weaker because the author was super new to published writing.

Magician: Apprentice & Magician: Master by Feist are great

Long before there was Harry Potter, Ged from A Wizard of Earthsea by Ursula K Le Guinn was discovering he had magical talents and going to wizard school. It’s a beloved classic for a reason.

A neglected series is Riverworld by Philip Jose Farmer. There are five volumes that are a great read.

All humanity is resurrected after death on the banks of a strange river. Each book deals with a real historical figure and the struggle to understand the mysteries of Riverworld. Each volume more or less follows characters from history (Richard Burton, Mark Twain, Cyrano de Bergerac and others) who embark on a journey to travel to the end of the River in order to solve the mystery of their resurrection. It's quite pulpy but very enjoyable.

The Kingkiller Chronicle trilogy by Patrick Rothfuss. It is not so much LotR becauseitt focuses on one main character. But it has a pretty clever and thoroughly thought out magic system and I for my part enjoyed the story. Link to openlibrary

Have you tried wheel of time?