There is a limit to the resolution of any optical system. That limit is called diffraction and I first ran into the term with astronomical telescopes. In photography, according to optical theory, any lens devoid of aberrations should perform best wide open. In the real world our lenses generally perform best (sharpest) stopped down slightly from wide open, performing best in the range of f/4 to f/8.
In film days we typically closed down our lenses to achieve added depth of field. The reduction of the circle of confusion created by the out of focus image on either side of the point of focus makes the image appear sharper over a greater area. This is still true, providing we do not exceed the diffraction limitation of the lens. The effect of diffraction limitation has a more obvious effect in digital capture than it did in film for reasons I will not pretend to fully understand. The result is an image that loses critical sharpness even at the point of focus. This is because the disc resolved by the lens exceeds the size of the capturing pixel resulting in loss of resolution. That means that optimum sharpness and depth of field are a trade off after you reach the limiting aperture.
The pixel size on a DSLR is a result of the capture resolution, and the size of the pixels related to the lens determines the effective diffraction limitation, not the lens itself. Therefore, the limits change as you put a lens on different camera bodies with differing sensor resolutions. The diffraction limitation of a particular lens of mine is nearly the same on a 10Mp APS-C body as it is on a full frame 22Mp body because of the difference in the size of the pixels themselves.
While it may be helpful to know what your limitations are for a particular camera there are many other factors that will have a greater destructive effect on your images. All optical maximums depend on solid support, shutter speed, ISO noise, and other factors even including the characteristics imparted by the raw converter used to process the file.
For further information I recommend visiting http://www.cambridgeincolour.com/ and searching for diffraction limitation. There is more information there than you probably really want, but the interactive charts can be useful in ballparking the optimum apertures for your camera.