Coming right up
There are sooo many Dragon books its ridiculous, but here's just a few that I've really liked or read.
Dragon-only universe:
Dragoncharm by Graham Edwards, followed up by Dragonstorm and Dragonflame (loved these books when I was in high school, it's been a while since I've read them now, but have read them multiple times)
Human and Dragon universes:
"The Last Dragonlord" by Joanne Bertin (one of my absolute faves) followed up by "Dragon and Phoenix", and "Bard's Oath" (which I've just ordered from amazon, can't wait)
Elvenbane by Andre Norton and Mercedes Lackley (I remember really liking this though have only read it once), followed up by Elvenblood, then Elvenborn
The Eragon series by Christopher Paolini, I wasn't too much of a fan and only read the first book, but I think there's about five.
Then there's The Ultimate Dragon, which is only a series of short stories, but one of those is a back-story about two Character's from Joanne Bertin's Last Dragonlord. So if you read those and like them, it's worth digging up the book to read that short story.
There's also The Dragonriders of Pern, by Anne McCaffrey, which I'm lead to believe is a huge series of books, though I've never actually read any of them.