First, you are not telling us the recipe(s), or your typical way of choosing and following them. Due to your reference to fat and calories, I suspect you might be choosing recipes with lower fat/sugar content than average, and possibly reducing fat and sugar in them. If this is the case, there is an important thing to note: your cake still has to be made up of mostly fat, sugar, and hydrated starch, with some eggs as binder. If the recipe creator or you added too much other stuff in order to reduce calories (which can also take the form of e.g. using whole wheat instead of the finest grade), you will get a drier, less cakelike result. If that's what you have been doing, you will need to get back to a more standard recipe.
Second, let's assume that you are using a standard recipe with sufficient sugar+fat. In this case, the most likely culprit is overbaking. You should be testing the cake with a toothpick or thermometer, not just sticking it in the oven for the time suggested in the recipe. Also, you might try to bake it at a lower temperature in case the outer layers dry out before the center is done. Assuming proper baking time and standard ratios, a cake won't be dry.
Third, let's assume that you are close to standard ratios but just a bit too far off, bake by doneness, and want to tweak just a little without getting more fat or pure sugar into the cake. In this case, you have two options (you can combine them too).
- add trapped moisture. Adding pure liquid (water, milk) won't help, but fruit purees are good. Applesauce is the traditional one. Slightly dessicated versions will work better than freshly pureed fruit, and high-pectin fruit works best.
- add emulsifiers. They make the cake feel moister. You can add yolks, pure lecithine or some other emulsifier if you have it in a pure form. The mayonnaise advice mentioned in another answer also works that way, as commercial mayonnaise contains chemical emulsifiers (physical ones won't work in a cake).
If all this fails, you can try a syruped cake as suggested by Jolenealaska, but while not unpleasant, it does have a very different mouthfeel from a standard cake.