I found some icons that would be a good fit to my iPhone app based on the features/scenarios that the app will provide, but noticed that an app in the App Store already use those icons. So question is, is it ok to use those icons again? Or in another way, are the icons from the App Store apps allowed to be copied and used in other apps that are owned by different organizations?
Icons are definitely not freely copy-able. Apps in the App Store still enjoy the copyright protections afforded under intellectual property laws in your region.
If you've found an app with icons that you're smitten with try contacting the developer about it. Often developers will purchase icon sets from icon factories like iconarchive.com (link omitted on purpose). These icon sets are licensed to you, for use in your applications, and come with the necessary license to allow you to redistribute and profit off any product that includes them. You can find free and paid-for icon sets out there. The developer might be forthcoming if they purchased their icons from a factory.
If the developer has designed the icons on their own they may choose to license them to you or they may say no. In which case: respect their wishes or you may find yourself on the receiving end of a cease-and-desist letter that prevents you from selling or giving away your app to the masses.