The Male Dragonfly is one of the 24 Golden Bugs in Twilight Princess. Its female counterpart is the Female Dragonfly. This bug can be traded to Agitha for a Rupee prize.
Collecting for Agitha
The Male Dragonfly can be found in Zora's Domain. Once Link enters the Zora's Domain area, go to the west side (Wii) or east side (HD) and climb the ramp. Floating atop some grass about halfway up the ramp will be the Male Dragonfly.
The Female Dragonfly can be found in Zora's River just south of Zora's Domain.