Compliments 
The way colors work together with one another is based upon their position on the color
wheel. You may understand a lot of these concepts without even realizing why. You know that Red and Green go well together, as they are the colors seen every year in every store as the Christmas season rolls in. If you've ever eaten in a fast food restaurant, you know that Red, Orange, and Yellow go well together. You know that Red and Blue go well together as those colors are seen everywhere - from the American Flag to Superman's costume. If you're a Carolinian, you know Purple and Yellow go well together, because you've seen them together as the school colors of East & West Carolina Universities. 
Basic complimentary colors are those found directly across from one another on the color wheel. The most known of these are: Red and Green, Blue and Orange, and Yellow and Purple.
(It's also no coincidence that these basic color compliments each contain a portion of the basic colors that introductory art students are taught to use as the basis of all colors: Red, Yellow, and Blue - or in television and movies: Red, Green, and Blue.) There are, of course, other colors that can be considered complimentary, such as Teal and Red-Orange, or Lime Green and Magenta.
Different Compliments
Split compliments and Triadic compliments are also seen on a fairly regular basis. Split compliments are complimentary colors (such as red and green) combined with one other color to the left or right of the first two. Examples pictured above: Red, Green, Teal; Orange, Blue, Yellow-Orange; Yellow, Purple, Magenta. Triadic compliments are three colors set at equal distances apart from eachother on the color wheel. Examples pictured above: Red, Yellow, Blue (whee!); Orange, Purple, Green. Analogous colors are three colors found directly beside eachother on the color wheel. Examples pictured: Red, Red-Orange, Magenta; Orange, Yellow-Orange, Yellow; Lime Green, Green, Teal; Blue, Violet, Indigo. 
Even if you don't remember what it's called when a company has Purple and Green for their main color scheme, or the wording presented above, it's always important to remember which colors look best together so your design doesn't turn out to be the most hideous thing on the planet. Remember: colors that are often chosen to go with one another are usually done so for a reason!
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