Basically just to put movies on it. I hate iTunes so I manage my apps on the device's App Store and I'm going to use Dropbox for pictures. So I try to avoid connecting it as much as possible.
Probably every other week, mainly as a back up. It seems that the software needs updating nearly every month..which is annoying since it takes so long...loving my iPad.
i connect the iPad at least once a day because i'm a photographer and i always have to transfer my pics from the Mac to the ipad. besides, the Mac is alot better to do images searches on the net.
Only to copy videos. I use the app fotomanagerpro to copy picture to my ipad/iphone and the computer.
Single ebooks are copied using the app filebrowser. Music to my iphone is copied with a free alternative to itunes. Apps are managed through wlan and itunes on the device.