Apple now includes an option for keeping your apps up to date automatically. Simply open the settings app on your phone and select the option for "iTunes & App Store".
About halfway down this page, you will see an option for "AUTOMATIC DOWNLOADS". Ensure that this is turned on for Apps and Updates.
This menu also includes the option to use cellular data or not. By default this is turned off, which means your app will only update when your phone is on a wifi network.
If you data plan allows it, you should consider turning this on.