Anne McCaffrey's Dragonriders of Pern

These compete with the Dark Elf series for my Favorite Fiction EVER.
The Characters are widely ranged, covering hundreds of years, and the different mentalities thereof. The Dragons are imagined in a whole new way, able to "teleport" from one place to another, and yes, even one time to another. In this series, like several others, the Dragons are bonded to a single human and will not continue to live if their rider is killed. I at first expected the idea of dragons fighting Thread(read:Destructive spores that dissolve anything and anyone they touch), to be boring, but the fact that the dragons are not against each other makes the story more interesting, and makes for some pretty deep intrigue.
One warning, there are some non-graphic sex scenes scattered throughout the books, so if you have kiddies be careful.
This is an excellent blend of Sci-fi and Fantasy, and I recommend it heartily