I'm not sure what you mean- I couple a halogen light and a Mercury arc lamp into a fiber on my microscope.
There are many kinds of fibers- single mode, multimode, light guides, bandgap, polarization-maintaining, etc. etc. etc.
A single-mode fiber is what most people associate with "optical fiber", and single-mode means a single transverse mode, which restricts the waveband. Multimode fibers can support a much broader waveband range, light guides (what I use with the halogen bulb/arc lamp) are not much more than "light pipes", and photonic bandgap fiber is really cool.
There's some technical issues with how to couple the light into a fiber, but it's sort of possible to couple nearly any source to any fiber- what light actually propogates down the fiber will depend on the fiber.
Welcome to PF, Chickenlittle.
I have to assume here that you're refering to information transmission. Any kind of light will propogate through an optical fibre, as you can easily see by looking at a fibre optic lamp. A modulated source is needed for any sort of information transfer. You can transmit Morse code just by turning a light bulb on and off. For the complexity of high-speed digital transfer, a coherent source is more readily controllable and more accurate.