I had a friend in high school who absolutely loved the Ann McCaffrey Pern series. I couldn't get into it too much but it may be an option.
Honestly I still say the Dragonlance series is one of the best out there. It was the series that got me into Fantasy to begin with back in High School and Margret Weiss is still one of my all time favorite authors. The new Dragonlance books by her are amazing. (A book has never shocked and disturbed me to the point of tears before I read one of her latest. That gets big kudos from me.) Though I'd start with the original trilogy. There's a ton of books, many by different authors (Which can be hit and miss) But I stand by Margaret Weiss and Tracy Hickman until the end. The new ones are just by Margaret Weiss which is fine by me. She was the one who really fleshed out the characters whereas Hickman was more involved in world building.
The two newest trilogies from her are the War of Souls and then the Dark Disciple. They take place about 80 or so years after the original series and almost all the original heroes are dead. However, the new characters are brilliant.
Of the whole series I would recommend the following in this order (I'm leaving out a number of them that really aren't important to story, but they do flesh out some characters)
Dragons of Autumn Twilight
Dragons of Winter Night
Dragons of Spring Dawning
(The following are continuation and in between storyline for the first three)
Dragons of the Dwarven Depths
Dragons of the Highlord Skies
Dragons of the Hourglass Mage
Time of the Twins
War of the Twins
Test of the Twins
The Second Generation (This one is ok, but I recommend it for continuity more than anything)
Dragons of Summer Flame
(These ones aren't awesome, but I'm listing them so you can get an idea of what goes on between the War of the Lance and the Chaos War. They're short and informative. Otherwise it can get confusing because the world changes so drastically. They're by Jean Rabe. They struck me funny because Skie the dragon's new name is the name of one of my characters in Aly's storyline. I was annoyed at first but then I figured it was pretty fitting so it doesn't bother me *laughs*)
The Dawning of a New Age
The Day of the Tempest
The Eve of the Maelstrom
(Alright now I'm listing the two newer trilogies that I really loved. These are a must)
The War of Souls Trilogy:
Dragons of a Fallen Sun
Dragons of a Lost Star
Dragons of a Vanished Moon
Dark Disciple Trilogy: (By far the best imo)
Amber and Ashes
Amber and Iron
Amber and Blood
Now there's tons of books. Here's the wikipedia link that lists all of them:
List of Dragonlance Novelsthere's tons, some are hits, some are kinda misses. It depends on who's writing as there's a ton of different authors.