Instead of copying or moving media around, why not stream it? That's what Plex Media Server lets you do. It allows you to quickly turn any computer into, basically, a media server.
Just download and install the Media Server program on your PC or Mac. It lets you import and organize your movies and music.
You can then grab a player app for your iOS or Android gadget. This lets you connect to the server and view your media.
There's also a player program for Macs and Apple TV. Plex support is even built into some LG TVs and set-top boxes. Unfortunately, there isn't a Windows player at this time.
The streaming works best over Wi-Fi, but you can also connect to your media server over the Internet. This is handy if you're away from home. Just remember that streaming media over a cellular connection will eat up your data minutes very quickly.
System: Windows XP, Vista, 7; OS X; iOS; Android