Very very rarely. I've done it maybe twice or three times since I first got the iPad 1. The iPad 2 seems to have the same longevity. However, this is what I did the first time.
Actually run movies, videos, and stuff for over 11 hours in one day. (Benchmarking the battery).
The only other times is if I actually have a real long session of intensive gaming for quite a few hours before it would drain. However, we're still talking over 5 hours, though I haven't perfectly benchmarked it. Usually, if full, I never even worry about draining the battery within a day even with intensive stuff.
What is the most intensive software I've run? Basically the higher graphic 3D applications, like.
1. Infinity Blade.
2. Deep space.
3. Dungeon Defenders (oddly, one of the highest demanding games, in particular for Disk space. Most games, particularly on the install, take way less.)
4. Real racing 2.
5. Order & chaos online.
There's more, but those are the general area of software that seems the most demanding. However, even running those games, the battery still lasts a lot longer than anything else, I've seen, running 3D gaming of that caliber. Even better, it generally remains cool. The HDMI connector, itself, seems to be warmer than the iPad even when doing the Real Racing 2 1080P mode.
During normal use, when I use it fairly often, we're talking 3 days between charges.