What can I do to fix/improve a dry cake?

No matter what kind of cake you've made, if it turns out too dry, you can moisten it with an appropriately flavored liqueur or syrup. Use a skewer to poke holes every inch and a half or so, then use a pastry brush to paint on the liqueur or syrup getting more into the holes. Coffee syrups come in sugar free varieties if you'd rather not add more sugar.

As far as what is happening, since it is happening with different recipes, I suspect your oven. Is it running hot? Use an oven thermometer to be sure that you are getting the temperature you want. Also, check cakes frequently in the last 10 minutes of baking, using the method recommended in the recipe to gauge the doneness. Usually, the toothpick test works. Stick a toothpick into the cake and remove. If there is no batter on the toothpick (a few moist crumbs are OK), then the cake is done. Cakes that are overdone will always be dry.

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.

A plain sponge or similar can be turned into a lemon drizzle cake (BBC, many other recipes available). Although this adds some sugar, the actual amount is small compared to the rest of the cake. For a really dry cake you might want to make the drizzle a bit runnier (less sugar) anyway.

Variations on this are easy. Orange and lime are obvious choices, I've had success with whitecurrants (though the topping was a little jammy).

Otherwise splitting the cake and filing it with something compatible has to be the way to go. Almost anything you add will include sugar, most will include some fat as well. You can seek out low calorie icing options if you really want, but it's already a cake. Any way you can get fruit in the filling/topping will help with both moisture and calories, with the more calorific part just to hold the fruit together. For inspiration you could look at a fraisier (pics via google). Note that many of these options change the keeping qualities of the cake (it might even need to go in the fridge).

An alternative to moistening the cake itself could be to serve it with something moist. I usually make a glaze/frosting if the cake itself turned out too dry. Sometimes (not always) the cake will not feel so dry when you eat it. It depends on the cake, serving with sauce or ice cream can also help.

Concerning the cause, other answers have good suggestions, I would like to add that it could be related to the ingredients you use. Different flours vary in gluten and protein (I think that is the cause) and absorb liquid differently. For instance, if you replace some wheat flour with coconut flour, you should add more liquid to the recipe.

The best and easiest way to fix this problem is to put the cake upside down when you get it out of the oven. Let it rest till it's cooled down.

Add mayonnaise to the batter. Don't laugh, Google it.