Stabilization can be especially helpful for telephoto lenses because telephotos not only magnify distant objects but also magnify the small movements of your hands as well which can lead to blurring in photos. While Image Stabilization can be helpful in situations where your subjects aren't moving (it does nothing to freeze subject motion) it does have limitations though.
Non-stabilized telephotos can give you quite good results provided you take some care when using them. The easiest approach is to use a stable platform like a tripod or monpod or a handy surface and use either a remote shutter release or the camera's timer to help avoid shaking the camera when you take the shot. You CAN also handhold a non-stabilized telephoto IF you take care to make sure your shutter speed is fast enough (having lots of light helps) and you brace the camera properly. There's a simple rule of thumb for picking a shutter speed but I'll leave the math for later.