Common wisdom says that you should shut off your lens’ image stabilizer when shooting from a tripod. There’s another saying that it’s safe to use on newer generation lenses, because it detects that the lens is steady and turns off the ill-effects automatically. Actually I belong to the former camp. When I compared my new non-L prime trio with the L zooms, I did a pair of test shots with my Canon EF 70-200mm f/2.8L IS USM (version 1, which I own for 9 years) for the sake of this post.
The pictures show the center of the image, where I focused with contrast detect focus and validated that the focus is spot on manually through live view (by executing a manual focusing step to see whether I can focus any better). The camera used was a Canon 5D Mark II, mounted on a sturdy Gitzo 1325 tripod and Arca-Swiss Z1 ballhead. The zoom was set to 70mm, aperture was f/8. These are unprocessed images straight from Capture One 6.4.2. Yes, these were shot on a cloudy day.
The first 100% crop is the non-IS version. As good as it gets.
And here is what happens if you turn IS on.
The bottom line: if you are seeking ultimate image quality and as such shooting from a tripod, then shut IS off (unless you test your configuration for yourself and that test proves otherwise – newer lenses can behave differently). It will also save some battery power!