Don't we all just love crayons? All the colors, the variety? Well, as we all know, most good animes don't just smack certain colors on their characters 'just because'. Colors represent different things. So I'm going to do my best to make a small list of what different colors represent and give some examples of where you'll see it. So, here I'll start.
Red
Red is most often thought of as a fire color. It can also be thought of as an earth color, but that is rare. It symbolizes strength, courage and power. Since it is also the color of blood it is most often associated with fury or strength ('blood boiling' type of thing).
Other than those most often thought of qualities, it also represents vitality, security and stability, and those who can survive.
In anime, characters that wear or are associated with the color red is Hino Rei/Raye from Bishoujo Senshi Sailor Moon/Sailor Moon. Ryo Sanada from Ronin Warriors/Samurai Troopers has the red armor.
Orange
Orange is an energetic color, full of enthusiasm and warmth. Strangely enough, it can be associated with fire, earth and water. Water is obviously much more rare to find though, since most people automatically think of orange as being in a fire. There is a such thing as 'orange water', as it is called.
Along with that, orange is a symbol for creativity, awe and being open to others.
Goku in Dragonball/Z/GT wears orange (sometimes a very reddish orange, depending on the picture). Kento Rei Faun/Shu Rei Faun from Ronin Warriors/Samurai Troopers has the orange armor.
Yellow
Brighter than orange, yellow is easily the color of the sun. Extremely radiant, exuberating energy with self-control, yellow is thought of as a joyous color. Often people who are in a bad mood or naturally gloomy may be irritated by such a bright color and not even know why. Yellow is a distracting color and it's use is often avoided in schools due to the way it unsettles students.
Due to the strength of the color it also shows inner strength and personal power. In it's flamboyant idealism is the basic concept of optimism, even if it does bother less optimistic people.
Aino Minako/Mina from Bishoujo Senshi Sailor Moon/Sailor Moon wears yellow.
Green
Most often used in nature, green is a very harmonious color. It's a simple, peaceful and compassionate color, that hints at very strong feelings. Green is the spirit of the heart, and is often the color for healers.
Among the emotions green shows it also has a sense of devotion. People using green as a symbol are often selfless and show unconditional love.
Kino Makoto/Lita from Bishoujo Senshi Sailor Moon/Sailor Moon wears green. As a side note, Kunzite (Malachite's original name) is a gemstone representing green. Malachite is also a type of stone. Seiji Date/Sage Date from Ronin Warriors/Samurai Troopers has the green armor. Raiel from Hamelin no Violin Hiki has a green and white costume.
Blue
The most common element for blue is water, but it can also be the element 'ether'. Blue is a symbol of intelligence ad tranquility. Along with that it's also a color for inspiration and confidence, people using blue for their color can express themselves creatively.
Freedom is another less used quality of blue.
Mizuno Ami/Amy from Bishoujo Senshi Sailor Moon/Sailor Moon wears blue. Vegeta from Dragonball Z also wears blue. Shin Mouri/Cye (or Sai) Mouri from Ronin Warriors/Samurai Troopers has the blue armor, and Hashiba Touma/Rowen Hashiba from the same show wears a darker blue armor.
Purple
Purple can identify with both the water and the thought element. More often than not purple is a show of royalty, mysterious and authoritative. It also shows the psychic awareness of a person, delving into the unconscious mind. Characters in purple usually keep themselves secluded and aren't necessarily dark characters, but private or isolated.
Purple strives for perfection, looking for wisdom and enlightenment. It's often that these characters are quiet spectators, observing what everyone else misses.
Meiou Setsuna/Tristra from Bishoujo Senshi Sailor Moon/Sailor Moon wears purple. From Vampire Princess Miyu, Larva's cloak is often colored with a dark purple (and I've seen lighter purple's used for it in pictures, as well).
White
White is an air element, and like purple can also be identified with thought. Though white and purple are similar, white is more simplistic, pure and clean. It's the simble of innocence and youth.
Characters in white are normally are honest people who do their best to live peacefully, and wish to have an understanding of life and people.
Not all characters stay within these boundaries. Just like with names, sometimes a character will have a name 'just because'. Plus, characters usually wear more than one color. Lina Inverse from Slayers/Slayers NEXT/Slayers TRY/other Slayers related shows and movies for example, is yellow and red. Quite suiting, actually.