Here are two book series that I have read.:)

The DragonKeeper Chronicles by Donita K. Paul- A fantasy series about dragons, five books in all, they are a Christian allegory of sorts.

Dragons in Our Midst by Bryan Davis- set in now a day times it’s about dragons in hiding, this series has very prominent Christian themes, beliefs and morals, there are four books in all(This book series is also followed up by another book series Oracles of Fire, this follow up also has four books)

Sorry if you do not want to read Christian book series, these are the only dragon books that I have read (I also read the first two books in the Inheritance Cycle, but you already have that down)
I'll be sure to post any other good dragon books down :)

Oh! I just remembered a few more dragon books that I read... (Wow... I just finished writing my last reply...)

Dragon Chronicles by Susan Fletcher- Three books about three different people who need to save dragons (I only read the first two, unfortunately, because the library near me only has the first two).

Well I've read...

A few books by Cradissa Cowell, she has done a few books about a boy called Hiccup and its set in the viking times, and Hiccup has a Dragon called Toothless, which isn't the most obedient dragon, its a really good collection, I don't know how many there are, but they are really good books.

Also there's Ice fire, Fire Star and the Fire Within by Chris D'Lacey
This is about Dragons who have been created by clay by a perticular women, and only a select few can see them for what they really are, there also really good books.

Hope thios helped!!

^^^ I've read the Chris D'lacey books, but( in my opinoin) I didnt like them very mutch.

one good dragon book is 'Dragon Slippers'- wich is about a girl who meats dragons and takes place in an imaginary time in an imaginary place.....
the sequel is 'Dragon Flight', then 'Dragon Spear'.

I have another series with dragons as a main part in them: the dragon codices. Like the silver dragon codex, the red dragon codex, the bronze dragon codex, the gold dragon codex.

Temeraire series by Naomi Novik
It's a combination of dragons and history it takes place in Napoleonic time ,the first book is called his majesty's dragon

The Dragonlance Chronicles, I swear there's at least fifty of 'em, and they most certainly are not short books. If you can stay interested, they will keep you busy for a while.

the Dragonriders of Pern & the Harper Hall of Pern, They're old, but very good.

I have more, but I can't think of the titles. :(