While there have been ways to make this happen before, Gmail now allows you to choose the inbox style that best suits you. Whether that's priority inbox, just your unread messages, or whatever, you now get to choose.
Once this option is added to your account, you'll get tabs above your primary inbox letting you switch between them. After about a week, and once you've settled on a style you like, these tabs will disappear (but you can always change it on your settings page). If you don't have this option yet, just be patient. It should be rolling out over the next few weeks.
New! Pick your favourite inbox style [The Official Gmail Blog]