Chronological Order of Pern Books

In the First Pass:
Dragonsdawn
The Chronicles of Pern: First Fall

In the Second Pass:
Dragonseye

In the Third Pass:
Dragon's Kin
Dragonsblood by Todd McCaffrey (release date to be announced)

In the Sixth Pass:
Moreta: Dragonlady of Pern
Nerilka's Story

In the Ninth Pass:
Dragonflight
Dragonsong
Dragonquest
Dragonsinger (overlaps with Dragonquest)
The White Dragon
Dragondrums (overlaps with The White Dragon)
Masterharper of Pern (overlaps with all of the above and more)
Renegades of Pern
The Girl Who Heard Dragons (short story)
(also the title of an anthology of short stories, not all of which are set on Pern)
All The Weyrs of Pern
The Dolphins of Pern
The Skies of Pern

Also note the following compilations:

The Dragonriders of Pern includes Dragonflight, Dragonquest, and The White Dragon.
On Dragonwings includes Dragonsdawn, Dragonseye, and Moreta: Dragonlady of Pern.

A Gift of Dragons is a collection of short stories which are mostly set in the Ninth Pass.