Summary: Full-fat yogurt creates a moister, denser muffin. Non-fat yogurt produces a drier, more aerated muffin.
Joy of Muffins has a lemon poppyseed poundcake muffin recipe (delicious), which calls for plain yogurt. It says quite explicitly: "Do not use non-fat yogurt."
I just can't help myself. I had to test it.
The batter was different from the start. The full-fat yogurt (on the right below) produced a smoother, creamier batter. The non-fat (left) was clumpy and thick.
The resulting muffins, though, differed more subtly. The full-fat muffin (top photo, right) was definitely denser and moister. The non-fat (top photo, left) was more aerated and dry. But the differences were small. If I weren't eating them side-by-side, I would never notice the difference.
Still, the full-fat muffin is clearly superior. Sigh. Just once, I want the healthier version to taste better.