I would say it personal choice, unless your trying to appeal to a certain group then it woulod be based on that groups preference. More often than not a monochromatic scheme is chosen because it appeals to a wide array of user who might happen upon your site.
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Consistency in websites is not just about colors. Having consistent colors but inconsistent font styles/ layout would still ruin your consistency. But, if color is the primary parameter you're juding your website consistency with, you could try Kuler from Adobe. A great tool for color palettes. You could choose from millions of pre-made combinations or you could even make one yourself.
Do take a look: http://kuler.adobe.com/