Original Series   *see note 1 at very bottom*
Spyro
Spyro 2
Spyro Year of the dragon
Spyro 4 Enter The Dragonfly
Spyro Season of Ice
Spyro Season of Flame
Spyro Attack of the rynocs

Hero Series *See note 2 at very bottom*
Spyro A Heros Tail
Spyro Orange
Spyro Shadow Legacy

Legend Series
A new beginning
Eternal Night
Dawn of the dragon

Now, im not counting skylanders, as skylanders really is nothing to do with spyro at all aside from characters making cameos (Sparx, Spyro and Cynder). Now, Skylanders is the main focus of Activision, however, Spyro and Skylanders is actually a different IP. One of these days its likely Activision *may* revive the IP once Skylanders Fad dies down. Spyro and Crash are currently abandoned IP`s.

*adding more later*

NOTES:
Note 1: The original series is based off of insomniac designs that spawned from Spyro 1 up until Attack of the rynocs. After that game, heros tail was a mini reboot, which changed several things.

Note 2: Heros tail is its own stand alone series. Evidence of this is: 100% new voice actors (Not counting Gnasty Gnorc or Sparx), new music composer, new storyline, and new focus. Also, the design of many characters were changed, and locations from past games were never mentioned once.