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iWork: Using AirPrint
Pages is a native iOS application that is part of Apple's iWork suite that can print directly to an AirPrint-capable printer. However, note that the option is buried in the Tools menu. Unlike Safari, the Share menu within iWork apps does not have a print option.
iWork Applications can store data locally on an iOS device, within iCloud, or from a cloud storage service that is compatible with WebDAV feeds.
Google QuickOffice: Printing
Google's QuickOffice for iOS works with their own Google Drive/Google Apps services and is capable of directly printing to an AirPrint-capable printer as well.
QuickOffice was purchased by Google in June of 2012 and once had the ability to store data in competing cloud services such as SkyDrive (Now OneDrive) and DropBox. It does not anymore.
If you don't have an AirPrint-capable device, but you own an HP printer, you might want to look into their ePrint software, which works with a wide range of their own printer models. Additionally, you can print photos and emails directly from your iPad, and can access a number of HP printers at public locations hosted by UPS, FedEx, Walmart and PrinterOn.