1. Seraphina by Rachel Hartman.
I love this novel to death. In this world dragons have the ability to shift into human form and therefore are able to have "relations" with humans... this creates halfbreeds. Our protagonist, Seraphina is a halfbreed. The novel follows her struggle in being one and also how she thinks it's driving her insane. Then she meets royalty and then the real issues begin.
2. A Song of Ice and Fire by George R.R. Martin.
So, yeah. There isn't really much dragon action at the beginning of the novel but when they appear it's epic. I think, although he has the most attitude, that Drogon is my favourite of Daenerys' dragons. The other two being Viserion and Rhaegal.
3. Talon by Julie Kagawa.
Ember is a dragon sent with her twin, Dante, to live amongst humans. However, the people of the Order of St. George have other plans for them. Until that is, Ember makes friends with one of them and things go a little pear-shaped. Both Talon and the Order of St. George have a bit of an issue when they aren't obeyed... to be honest that's putting it awfully lightly.
4. Eragon By Christopher Paolini.
Eragon is a dragon rider, one of the last. His dragon is named Saphira and together they attempt to battle and hopefully overthrow the tyrannical ruler Galbatorix.
Those are just some of my favourite Dragon novels.
Which do you like?