My experience is that IS works more often than not... but is not foolproof. I use it, but I try to avoid relying on it. In other words if I can shoot with a fast enough shutter speed that I wouldn't need IS, then I will.
If you think about the mechanics of how IS works, it makes sense that it can only control a limited amount of movement. Elements are physically moving to compensate for your movement. At some point the elements hit the limit of travel within your lens.
I've seen some lens reviews which specifically test for IS performance... e.g. shooting at 1 stop under, 2 stops under, and so on to see how far they can push the IS system and still get acceptable images. Nearly all lenses with IS will do great at 1 stop under and usually also 2 stops under. Many lenses start to become much less reliable at 3 stops under and few lenses perform well at 4 stops under even when the IS system is rated for 4 stops (although there's often "some" improvement over no IS at all... you do still see some motion blur.)
It should be noted (because I occasionally see this mistake) that IS only helps correct for camera movement... not subject movement. I recall seeing a Canon lens brochure showing off IS where they were taking a picture of a child on a swing and showed the difference between IS and no IS. It was a HORRIBLE example (great to sell lenses though!). A child on a swing is moving forward and backward like a pendulum... that would have been a MUCH better photo to show off the difference between single focus and continuous servo focus (aka Canon "One Shot" vs. "AI Servo" or Nikon AF-S vs. AF-C). The image implied that the IS was correcting for that movement (and of course they showed a blurry "without IS" shot and a sharp "with IS" shot.) With marketing like that, it's no wonder people are confused about what it does and how it works.
If I'm really concerned about motion blur, I'll use IS, but I'll also consider how I might be able use a stable platform (tripod, monopod, resting the camera ledge, railing, lean against a pillar, etc.)