For a less classic but more dragonific Tolkien work, there’s always Farmer Giles of Ham. It’s about a farmer who fights a dragon. I read it to my kids and they seemed to like it.
Guardians of the Flame series by Joel Rosenberg. I’m not sure how it holds up but I recall it being a bit smarter than average fantasy when I was young, although it does start out with the ultimate cliche of RPG players being transported, but it’s better than it sounds. Lately I’ve been reminded how shitty my tastes were when I was young, however.
And now that I think about it, the dragon is named Ellegon, which ain’t too far from Eragon, now is it?
The Guardians of the Flame series is really quite enjoyable. Some stuff is pretty cliche, but I like the way the characters grow and interact. They’re not entirely one dimensional.
The dragon is not a key part of the books, but he does frequently show up and play an important part. And he’s quite amusing, such as when he’s the giant pool toy for the kids in the town swimming hole :).