For devices that don't officially offer any user-accessible file storage, the iPad, iPhone, and iPod touch do a surprisingly good job of handling attachments to both incoming and outgoing email messages.
Usually, an incoming message that include attachments show a paperclip icon by to the sender's name in the message list. Without any additional software, iPhone OS devices can natively view (or play) a wide variety of file formats, including the following:
Graphics: JPEG, GIF, PNG, TIFF
Audio: MP3, AAC (.m4a), AIFF, WAV
Office documents: Word, Excel, PowerPoint, Pages, Keynote, Numbers
Universal formats: PDF, ...