A prominence (also known as a filament when seen as against the photosphere where it appears darker) is a big bunch of plasma hanging above the surface suspended by the magnetic field. Sometimes, but not always associated with active regions (sunspot groups). When seen against the edge of the disk they show up in H-alpha light looking like hedges, licks of flame, arcs, loops and so on.
Prominences tend to hang around for some time (hours, days) as they evolve whereas flares are small, highly localised, highly energetic (practically explosive) events of seconds to minutes duration, occuring in active regions where there is a high magnetic field (specifically, areas of magnetic shear).
CME's are somewhat like big prominences that have broken off and are hurtling into space. I don't really know that much about them.
I'd say it was OK to call a CME is a run away prominence. But, I'm not sure that description extends to flares (well, IMO - Turin might be on a different train of thought to me).
At least as I understand it, flares are pretty different being the sudden release of magnetic energy by reconnection, whereas prominences are merely dense gas being supported by the magnetic field. They are often associated though.
A good website to take a look at might be http://science.msfc.nasa.gov/ssl/pad/solar/default.htm [Broken]