Physicist specialising in optics here.Do image stabilisers decrease image quality?
Yes. All other things being equal, they do, and for two reasons:
1. A certain optical formula requires a certain number of elements. Adding extra elements above the minimum required causes problems, such as extra internal reflections and extra aberrations or distortions which then have to be corrected by altering the optical formula. The overall formula is then no longer perfectly optimal.
2. The IS group puts extra constraints on the design of the rest of the lens. In the case of telephotos there is usually plenty of space available for an IS group, but wide-angles are much more crowded. Inserting IS forces the designer to reshuffle the main optical elements and make certain compromises in the design.
Here's the more interesting question:How much do image stabilisers decrease image quality?
It depends. It depends on the skill of the designer, and whether he/she is allowed to employ expensive materials, expensive lens coatings, and strict manufacturing tolerances. There aren't too many examples of pairs of lenses which are identical except for addition/deletion of IS. Canon's 70-200mm f4 lenses (figure below) are superficially identical, but actually have slightly different optical formulae. In this case the (more expensive) IS version happens to be slightly better.
So if you're willing to pay for it, IS can -- in certain circumstances -- have little or no significant effect on image quality. However, even with the best designers and most expensive manufacturing, there are physical limits. Certain non-IS lenses will never have IS counterparts which are as good.