Shooting multiple shots like this is certainly common, but it's not optimal. As your skills improve, you'd like to see your consistency improve, too. Shooting digitally, we're lucky that multiple shots cost next to nothing for us, but you want to move away from using that as a crutch.

Instead, try to understand why you're seeing variation from shot-to-shot, and then give thought to whether this is something you can address proactively. It sounds like you've taken steps to stabilize the camera, which certainly helps in some scenarios. In other cases, though (a moving subject, for instance), stabilizing the camera won't help you too much. Finding the right combination of aperture, shutter speed, and ISO settings is a journey itself, as it will vary from one setting to the next.

Your performance as a photographer will improve markedly as you learn to manage these settings rather than to hope that one of a set of shots gets it right. You're clearly moving in the right direction -- keep it up! Over time, your consistency will improve, and you'll find yourself working on artistic aspects of your shots more than technical aspects.

As AJ mentioned, there may still be settings where you want multiple shots to capture a facial expression or an action sequence. You might also find yourself dialing down shutter speed for something like a panning shot which can bump your "reject" rate again while you learn techniques for successful panning. In these cases, though, you'll be shooting multiple shots deliberately for a good reason -- not just out of habit.