Using a barbell for compound movements is extremely beneficial in building muscle. Something that is just as important is using single side exercises to be able to ensure that both sides of your body are not only balanced, but strong. Below are some examples as well as reasons to train each side of your body separately:
1) Examples: Single Arm Row, Single Arm Bench Press, Single Leg Squat, Step Ups, Single Arm Lat Pull Down
2) Discover Imbalances: If you are always doing barbell exercises, you may not notice or feel one side weaker than the other. The most common would be the deadlift. When people mix grip a deadlift, this demonstrates that one side may be weaker not only in grip strength, but back strength as well. If then you try to do a single arm dumbbell row, most people will discover that they have a weaker arm. This is important because a weaker side can cause injury if not addressed.
3) Improve Compound Lifts: If you have a weaker side, normally your compound movements such as a bench press will eventually be restricted by the weaker side. Building up the weaker side will then in turn help your compound lifts in the long run.