@ submariner- The problem with cherry wood is that it is acidic. It will lower the pH of your soil, making it unbearable for many plants. Ash form cherry wood species has the same effect on the soil as pine needles and birch. Some plants like nightshades and blueberries will thrive in acidic soils, but most plants will suffer.
Besides ash from cherry and a few other species, most other wood ash is good for your soil. In fact, mixing ash into the soil is a good way to remedy acidic soil composition. Mix in maple, ash, or oak ash into garden soil to raise the pH of your soil. You can also mix one tablespoon per gallon of non-cherry wood ash to raise the pH by one.