Here is a PDF giving the order in which to read the books.

The following list is from http://en.wikipedia.org/wiki/Dragonriders_of_Pern#Original_trilogy

Original trilogy

Later collected in an omnibus edition. These stories take place immediately before and during the Ninth Pass.

• Dragonflight (1968; composed in part of McCaffrey's first two Pern novellas, Weyr Search and Dragonrider, originally published in 1967)
• Dragonquest (1970)
• The White Dragon (1978; although published prior to Dragondrums, The White Dragon continues the adventures of certain Dragondrums characters; McCaffrey recommends reading Dragondrums first; The White Dragon incorporates McCaffrey's story "A Time When")

[edit] Harper Hall trilogy

Later collected in an omnibus edition. These stories take place immediately prior to and concurrently with those depicted in Dragonquest and The White Dragon.

• Dragonsong (1976)
• Dragonsinger (1977)
• Dragondrums (1979)

[edit] Other novels and anthologies

• Moreta: Dragonlady of Pern (1983; both this and Nerilka's Story are set at the end of the Sixth Pass, centuries before the events in Dragonflight)
• Nerilka's Story (1986)
• Dragonsdawn (1988; first in chronological order, depicts the colonization of Pern, the First Fall of Thread, the creation of the dragons, and the colonists' move north.)
• "The Impression" (1989; short story included in The Dragonlover's Guide to Pern)
• The Renegades of Pern (1989)
• All the Weyrs of Pern (1991)
• The Chronicles of Pern: First Fall (1993, anthology set mostly after Dragonsdawn)
• "The Survey: P.E.R.N." (originally published in 1993 as "The P.E.R.N. Survey")
• "The Dolphins' Bell" (originally published in 1993)
• "The Ford of Red Hanrahan"
• "The Second Weyr"
• "Rescue Run" (originally published in 1992)
• The Dolphins of Pern (1994)
• Red Star Rising (1997) (called Dragonseye for U.S. release; set at the beginning of the Second Pass)
• The Masterharper of Pern (1998; prequel to Dragonflight and the other works of the Ninth Pass)
• The Skies of Pern (2001)
• A Gift of Dragons (2002 anthology collecting previously published stories and a new story)
• "The Smallest Dragonboy" (1973; short story previously collected in Get Off the Unicorn)
• "The Girl Who Heard Dragons" (1986; short story collected in both The Girl Who Heard Dragons and A Gift of Dragons)
• "Runner of Pern" (1998 novella set, like Masterharper of Pern, some time before the events of Dragonflight; collected in Legends and A Gift of Dragons)
• "Ever the Twain" (2002 short story original to A Gift of Dragons; time period unclear)
• "Beyond Between" (2003 short story in Legends II: Short Novels By the Masters of Modern Fantasy, Robert Silverberg, ed.; set after the events of Moreta)