Is it necessary to ground an outlet?

If the receptacle has a ground terminal (green screw) and has three prongs, you must connect a ground wire if it is a new installation.

There is one exception to this: if the three prong receptacle is fed from the LOAD side of a GFCI receptacle, it is not required to have a grounding conductor. This is because the receptacle is considered to be protected by the GFCI's function. In addition the GFCI itself is not required to have a ground connected. In these cases the receptacle needs to be labeled "no equipment ground" on the wallplate.

If this is existing, you are usually not required to correct things that were not originally done to code. However a three prong receptacle should not be used as such if it does not have a grounding conductor connected. This would lead to a false sense of grounding and safety.