First -- there are a couple of recipes where you melt the butter and combine it with the eggs and liquid, then mix with all the other ingredients. It's really easy, and only a couple more steps than a box mix (especially if you have a digital scale and don't have to get out the measuring cups). Just pm me if you want the recipes.
Here are a couple tips I've discovered for box mixes..
If the recipe calls for oil, replace it with melted butter. If you want a rich butter flavor, brown the butter. For each stick of butter you use, add 1-2 Tb oil. If you use less than 1 stick of butter, I'd not worry and just add 1 Tb of oil. 1 Tb of butter has less fat than 1 Tb of oil, so you need to add some extra fat.
Like other people have mentioned, add your own extracts. Vanilla for yellow/white cake, vanilla and coffee (can be instant espresso powder, dissolved in liquid) for chocolate cakes.
For the liquid, use buttermilk. Or if you want it very moist and tender, use half milk/buttermilk and half sour cream.
Last -- add ground nuts/nut butters. Almonds and hazelnuts would be great, and add a subtle depth of flavor. If using nut butter, mix into eggs so it is distributed throughout the cake and not lumpy.