Stardrops cause a permanent increase in your energy and are well worth pursuing. There are seven available in the game.
Treasure chest, mines floor 100
From spouse when at 13/12 hearts (13th is hidden)
For sale for 2,000 stars at the fair
From the statue in the secret woods when given a Sweet Gem Berry
Bought from Krobus for 20,000
Reward for catching all the fish
Reward for donating all possible items to the museum