Blue

Blue is Percy Jackson's favorite color and is also a kind of running gag throughout the series.

History
Gabe Ugliano once told Percy's mother, Sally Jackson, that there was no such thing as blue food. From that point on, she went out of her way to make blue foods to prove Gabe wrong. She would always bake blue cookies and buy blue candy for Percy, or she would make a blue cake on his birthday. Also, Percy's favorite color is blue. This could be because his father's domain is the sea, therefore blue, or simply because his mother making blue foods.

The Lightning Thief
Sally always made blue food for Percy. When Percy came home from Yancy Academy, his mom brought blue candy from the sweet shop, Sweet on America. To Percy, nectar tastes like his mom's homemade blue chocolate chip cookies. Also, when he first had dinner at Camp Half-Blood, he asked for his mom's "Blue Cherry Coke" to appear as his drink.

The Battle of the Labyrinth
Percy's 15th birthday cake is blue.

The Last Olympian
Percy promises his mother that if he survives, he would give his mother some sort of sign, "something blue." After Kronos is defeated, he asks Zeus to light up the top of the Empire State Building blue to let his mom know that he is safe. Without any argument, Zeus grants Percy's request.

Later, Annabeth brings Percy a birthday cupcake with blue frosting which, according to Percy, looks "like a brick with extra blue cement," when Annabeth told him that Tyson helped her bake the cake.

The Son of Neptune
When Percy is at Camp Jupiter eating dinner his first night, one of the aurae gave Percy a blue drink with his dinner. Hazel didn't understand the meaning of the blue soda, but it seemed to make Percy happy.

The Mark of Athena
While at the dinner table, Piper notices that Percy is eating an all-blue pie which includes the frosting and the filling.

Trivia

 * Blue is one of the primary colors and on the visual spectrum it's between green and violet.