I like the colors and the boldness of the design. I also like the contrast between the lettering type ("Zanthia" vs. "Marketing").
The design must work on a white background though. Please place this logo on a white background.
Additionally, I would like to see a font with the same trailing bottom line for the Z (underlining effect for "anthia") with a slightly less fluid text - something a little more hard-edged.
I definitely like #18. It is simple, elegant, and easy to read. I could see the logo being used as the stand alone "Zanthia" and for sub-businesses (e.g., "Zanthia Marketing", "Zanthia ________", etc.) - exactly what I want.
I think the colors fading in #15 look cool, but I would like to keep it as simple as possible - one color.