If you don't use the free service DropBox already, you're missing out on one of the best online services for syncing and sharing files. The fact that there's a free iPhone app available for the service is just the icing on the cake of awesome they've created.
The app works by letting you access all your files stored on Dropbox. You log in with your details, and then you can browse through your collection of files, photos, songs and anything else you've got stored up there. You can send and share files directly from within the app, and mark files as favourite so they are downloaded to your device for fast, offline viewing. You can also add photos and video directly from your phone to the service.
The latest update includes both retina support and caching of files, so you don't have to redownload files you've already viewed.
All told, for the grand total of nothing, you get 2GB of storage, plus bonus storage if you get other people to sign up. Then there's the free desktop and iPhone apps to access your content.