I leave it on unless I have a good reason to turn it off, which is rarely. Some older lenses have IS that gets upset with tripods and should be disabled when used on one. IS drains batteries faster...but with a pair of batteries in a grip that's not really much of a concern.
I have never seen any indication that it degrades anything at high shutter speeds or that manufacturers recommend turning it off for high shutter speeds. Indeed, manufacturers recommend it be used just the way I use it. It's true that it's less necessary at faster shutter speeds, but it'll still improve image quality at faster shutter speeds, even if only incrementally so.
Oh -- and you'd have to be a real manly man to get sharp images with a 400 handheld at only 1/250 without IS. I doubt I'd even try at less than 1/600 without IS and probably wouldn't feel confident at less than 1/1000. But with IS...well, I was playing around one night long after I got mine. I sat on the ground, braced my back against a wall and my elbows on my knees and took a handheld photo of the Orion Nebula that showed no motion blur. Clouded with lots of urban light pollution, yes...but the Orion Nebula! Handheld! Photograph! Without motion blur!