Dear Ted, Here's a good tip for you mate. If your in doubt, use adhesive to cover old tiles and replace new ones, but noting also if your going to increase depth of anything where old tiles are level with any surfaces. Eg sunk in soap dish in bathroom. You don't need to crack old tiles but if you can score them by using the edge of a screwdriver to scratch the tile surface then it should help. It is advisable not to go too deep as you'll go into the biscuit (plaster part of tile) but by using a good adhesive for tiles should be sufficient for tiling. good luck and make sure everything will be level before you start work.
Anthony Tovey, September 2010