The absolute best place I've found for tile info is at this place:
John Bridge forum
There are several pro's here besides John himself, and they will bend over backward to answer your questions.
To give a quick and dirty answer, if you have cushioned flooring, it MUST be ripped up. Otherwise you could run new overlayment over it if the total height isn't too much as someone else already pointed out. There's more details to be determined though like what kind of tile, the span of the floor, and the deflection of the floor. For instance natural stone can't be used without reinforcing the floor in most cases. It's not that the floor will collapse, but that the floor will flex too much and crack the stone.
Check out the forum above. Great place.