Did a quick search around and it seems my memory serves me ok here. Lenses do vary in what aperture is sharpest but factors such as diffraction (to do with the light wavelengths) causes sharpness to fall away at higher apertures. Chromatic Aberration can play it's part as well.
Some lenses are actually sharpest at f-stops around f4 or f5.6 but a general rule of thumb is apertures around 2 or 3 stops down from the minimum aperture of the lens is usually best.
So working in full stops, and generally speaking only, using f8 - f11 (some lenses may allow slightly lower or higher) is likely to produce the sharpest results.

Maybe someone here knows much more about it than I (I've only looked into it briefly here and there over the years) and correct me or add to what I've said?