Landscape for most things, though I will use portrait for all reading (Kindle/Zinio, etc), and sometimes for Zite and Flipboard, though I use them in landscape more often.
When I got the iPad 1, I used it mostly in portrait orientation. Now that I have an iPad 4 with a smart cover, it's mainly in landscape orientation to take advantage of using the cover as a stand.
Portrait, unless I'm typing with the on-screen keyboard or watching a video. As strange as it was to me that Apple chose a 4:3 aspect ratio, I've come to appreciate it now that I have an iPad. It's even nicer on smaller screens, as the Nexus 7 feels like a large phone while the mini feels like a small tablet. Admittedly, this is based on a brief handling of both devices.
I found it easier for myself to type in portrait mode. Maybe it's because I'm not a huge fan of the split keyboard or I'm just used to the thumb placement from my iPhone, but it works for me. I used landscape mostly for videos and when I'm reading something that I want to make bigger, although the safari plug in for increasing fonts and Mercury browser have rendered that easier in portrait, too.