Why does Naruto's headband change color? In Naruto Part 1, Naruto's headband was blue. In Naruto Shippuden, his headband was black. In one of the movies, it was red. A shinobi's headband symbolized who you are loyal to, so is there any significance to the headband's color, and if not, why was it repeatedly changed?
As Kuwaly state, there does not appear to be any significance in the color of their Headband's strap. The most common of all colors are either the blue or black

Navy Blue: The most common colour of forehead protectors. Many ninja keep this colour for the entirety of their ninja career.
Black: The second most common colour of forehead protectors. Some, such as Naruto Uzumaki, even switch from blue to black after the timeskip

Now the reason to why they change colors can be due to either

They do need to be replaced from time to time, especially after difficult training
They simply out grown of them, and want to change the color

In Shippuden episode 6, when Naruto is talking with Iruka over ramen, Naruto says to Iruka

The cloth on the precious Headband you gave me got all tattered

So given that information, Naruto changed his headband due to the fact that it was simply torn and needed to be replaced