Do I have to put cement backer board down before laying ceramic tile or can I go over existing vinyl floor?
There are a few factors that need to be considered. What is your subfloor? If its concrete and the vinyl is secured very well, then you can lay over it provided you put an acrylic additive in your thinset. This will help the bond to the vinyl. Also by doing this the vinyl will act as a crack supressant to the tile and protect against any cracks from your subfloor moving up to the tile. If you have a wood subfloor, you should remove the vinyl, install a 1/4 backerboard(not 1/2) and then install the tile with a modified thinset.
you can go over your old vinyl floor, just make sure its clean and flat and has no chance of infiltration. If you can't assure its steadfastness take it up
you need backer board because the initial cement that you lay the tile with will not stick to vinyl. The vinyl is unstable and will not take the grout either - years later you will have cracking heaving mess. Also you need a level area and vinyl tends to buckle and so forth.
I would worry more about whats under the vinyl. If the subfloor is just 1/2 plywood, it will move up and down when walked on. It may not be measurable with the vinyl but it will with hard ceramic tile. Your tiles and grout will crack. Most ceramic tiles require at least a 3/4 subfloor. Ceramic adhesion will not be good either over vinyl.
To start the purpose of cement board/hardibacker it gives you a solid base for the mortar,tile and grout to set on. When you a tiler places tile on wood subflooring the floor moves far more thus will short term and long term allow the tile to flex. Tile , mortar and grout will not and does not stand up to flexing. It starts with your grout cracking and crumbling, which allows the tile to move more breaking tiles and mortar giving out. Save your self the heartache I use hardiback concrete board its 1/4 thick. Commonly the tile is a 1/4 and you will be using a 1/4x1/4x1/4 mortar so you somewhere around 3/4 give or take 1/8 . If the room your tiling transitions higher already than adjoining rooms i suggest tearing out the existing flooring and starting @ the sub-flooring if possible. typically under any vinyl flooring is a prep board louin installers staple and glue it down its a nightmare to remove. but the end result of your tile job is professional. Good luck