I’ve enjoyed a lot of Margaret Weis and Tracy Hickman’s works. The Dragonlance Chronicles trilogy was one of my first entries into the fantasy genre as a kid, being interested in D&D at the time may have helped with that. I also really enjoyed their series The Death Gate Cycle. In a similar D&D vein, R.A. Salvatore’s books in the Forgotten Realms setting are pretty entertaining.
Jim Butcher’s Codex Alera series is a great read, though it seems lots of people have some trouble with the first book, The Furies of Calderon. I think it’s just getting into this world and the way magic (called furycraft in the series) works takes some time. It’s a lot more political that your average fantasy, too. After the first book, though, the other five are just a joy to read. Also, Butcher’s Dresden Files series is one of my favorite series, though it’s urban fantasy, rather than the high fantasy of Tolkien and Rothfuss.
Brent Weeks’ Night Angel Trilogy was enjoyable when I read it, though I must admit after a number of years now, I remember virtually none of it. Time for a reread!
Terry Goodkind’s Sword of Truth series, starting with Wizard’s First Rule is overall really good. The books vary in quality and do get very dark. I could see some of the content being very off-putting to some people, so your mileage may vary with these, but you know the 18-year-old in question and will be a better judge of such things.
For something a bit more comedic, Jim Hines’ Goblin Quest takes the typical D&D dungeon crawl and shows it from the viewpoint of one of the goblins who lives there.
Terry Brooks’ Shannara series is pretty good, though the first book, The Sword of Shannara is essentially a beat for beat copy of Lord of the Rings. He does better with the following books, and I really remember liking the quartet of books starting with The Scions of Shannara.
And, of course, there’s A Song of Ice and Fire.