It is not too big of a chore to remove backsplash tiles. The biggest consideration is inflicting the minimal collateral damage to the surrounding area because that will just mean more work for you in the long run.
The first thing you need to do is survey your tile backsplash on your countertop. Either the tiles on the backsplash intersect the countertop tiles at a ninety degree angle or the back splash tile is equipped with a small lip at the bottom that incorporates the angle to make a smooth transition to the horizontal.
In either case, the first task is to chip out the grout between the backsplash tiles and the horizontal countertop tiles. The best way to do this is with either a special grout removal tool or just a small bladed screwdriver with a hammer or mallet to carve it out.
If you have a lot of area to do, Dremel now makes a bit that is especially made for grout removal and the attachment is equipped with guides to keep from drifting and eating into the ceramic tile.
Once you have removed the grout from the grout line, you can begin to remove the backsplash tiles. How carefully you work depends on whether you want to save the tiles and how much reconstruction work on the underlying sheetrock you are willing to do. My recommendation is to take it slow and cause the least possible damage to th surrounding area.
Easy Does It
Begin by working a putty knife under the edge of an open sided tile and gently lift up. If progress is impeded, hold the putty straight on to the tile and top the butt with a mallet to try to separate it from the sheetrock.
Continue working in this fashion, tapping and lifting, until you get the first backsplash tile free. Now you will have a good idea of how much of a fight the tile and mastic are going to put up during this operation.
Using this kind of operation, attack first one row and then the next. Soon you will be done. The important thing here is to try to minimize damage while maximizing the number of tiles you successfully remove.