There are many types of lens aberrations. Examples of the most common are described here. For a nicely done technical explanation of aberrations, see https://www.vanwalree.com/optics.html.
Note: some of the images on this page may be clicked on for a larger version.
Chromatic aberration (CA) (red/cyan or blue/yellow color fringing on edges) is present on many lenses, particularly wide angles and long telephotos, but also on less expensive lenses of all kinds. It remains a persistent flaw in many lenses, even some expensive ones, and degrades sharpness and clarity. There are two types of CA. One type improves by stopping down; the other does not. Color fringes are not always obvious, but even when non-obvious, they can cause the image to have a slightly blurred look, because Bayer Pattern interpolation is forced to guess at the actual color.
Some types of CA can be corrected in software. Nikon Capture provides the best implementation of any tool on the market, requiring only an on/off setting that is effective even for images taken using a shift lens (see Nikon Capture’s Color Aberration Control). But of course Nikon Capture only works for Nikon NEF files.
Adobe Photoshop CS 2 offers several lens-correction features, including its chromatic aberration correction. If you like the Adobe Photoshop Capture Raw tool, then this may be the answer if you are a Canon shooter. Its much more “fiddly” than the Nikon Capture implementation, a real hassle when mixing different lenses and cameras.
Flare manifests itself as a bright haze over some or all of the image. It tends to be more of a problem with telephoto zooms, but it can occur with any lens, depending on the design. This example was shot with an otherwise superb Schneider lens with a diaphragm that is quite reflective (not matte black). It was not designed for digital use, and the flare results not from the optics, but from an internal reflection between the sensor and the lens element(s):
Ghosting usually manifests itself as a bright image of the lens aperture. With modern multicoated lenses, ghosting is not usually a problem except when shooting directly into the sun, as with the Nikkor 10.5mm DX fisheye image below (click for larger version).
Distortion might or might not be an issue, depending on the subject matter. When shooting architecture or products, it can be a serious problem. If the distortion is very strong, it might even be troublesome for portraits and everyday subjects.
Distortion can take any variety of forms: barrel, pincushion, moustache or other oddball types. In zoom lenses, it often varies in type and amount depending on the focal length. It can also vary with focusing distance.
Here is an example of barrel distortion; notice that in the center the red line is flush with the top, but curves down at the left and right edges:
Below is an example of distortion in a lens designed (ostensibly) for architectural photography (a particular shift lens). The distortion is obvious, creating a deformed structure that can’t pass muster for professional work.