Answer:
A purely scientific answer is that there are no more colours beyond what you see in a rainbow. The rainbow constitutes the visible spectrum, meaning that it is the only part of the electromagnetic spectrum that is visible to the human eye as light.
Beyond the red 'end' of the spectrum is Infra Red Radiation and beyond the violet 'end' is Ultra-Violet and beyond that X-rays. There is a Wikipedia article about the electromagnetic spectrum here:
http://en.wikipedia.org/wiki/Electromagnetic_spectrum