I haven't used iTunes on a desktop/laptop for ages. I agree with quite a few people that it's pretty annoying that you can't easily transfer an MP3 or ringtone to your phone and simply play it (or you have to buy it via iTunes).
Also the Mail and Music app (attachments possibilities untill iOS8 are almost not there) lack a lot of functionalities.
I do love my iPhone and iPad however because of the stability and speed of the devices (both hardware and software).
Below you will find my go to apps/widget that i love to use to get to my files (documents, music, video).
Music (offline or online):
MixRadio (smartradio),
Hype Machine (discover music),
Soundflake Pro (remixes), AudioTube (removed from the App Store, for
cache/download YouTube music),
CloudBeats (listen via cloud, grab from cloud and listen offline)
Video (local NAS, online or offline): AudioTube (for
cache/download YouTube, removed from the App Store),
Infuse 3 Pro (from NAS)
Documents/Files: Documents 5 (e.g. view/search PDF stored in the cloud on e.g. Dropbox, Google Drive or iCloud Drive, download files from internet),
FileBrowser (full or
lite),
Transmit for iOS (FTP),
Coda for iOS (text editor),
Easy Annotate (show 2 documents side by side stored in the cloud) or
Side by Side For both no need for a recent iPad to have this Split View option!
Coding:
Prompt 2
E-mail: Spark (iPhone),
CloudMagic (iPad) are great with attaching/saving files (to and from cloud storage)
see
Quick access:
Launcher widget (notification center),
Workflow,
Launch Center Pro (iPhone version),
Drafts 4,
Parcel
Internet Browser: apps that can show multiple website at once so some sort of Split View (also with an old iPad or old/new iPhone - uSurf only) which are e.g.
Side by Side or
uSurf Universal.
I also love the custom share extensions (extensibility) that is offered in quite some apps since iOS8. See also
this topic.