There are 32 heart pieces that can be found scattered around Hyrule, constituting eight additional heart containers for the hero. Here's a breakdown of their locations:
Ordon Village
Relic Collector's house in Hyrule Castle Town
West Faron Woods
Floria Peninsula, after defeating the Floria Babas
Hyrule Field, after defeating the Peahat swarm
Hyrule Castle, second floor
Kakariko Inn, second floor
Gerudo Encampment
Sewers, beneath Ordon Ranch
Hyrule Field, under a rock pile
East Faron Woods
Beach, after defeating the Giant Crab
Southern end of Lon Lon Ranch
Hidden Village
Snowpeak, on the ice
Zora's Domain
Death Mountain, just south of Septen Heights
Death Mountain, south of Goron City
Desert, after defeating the Lanmola
Death Mountan, after defeating the Lynel herd
Zora's Domain, after defeating the Pit Pincers
Ordon Village, after completion of the Gaira-Deacon side quest
Lon Lon Ranch, inside the barn
Septen Heights, inside a house
Snowpeak, inside an igloo
Kakariko City, in the Alchemist Alehouse tavern
On an island west of the beach
Subrosia
Three Eye Rock
King's Tomb
Island Palace
North Castle
Good luck in your search!