How cold should the air be that comes out of the house's ducts with the air conditioner on?

The air coming out your vent should be about 16 to 20 degrees cooler than the air being sucked into your unit through the return.

More Information:

I usually set the unit to where it blows out at about 55 to 60 degrees. Any cooler than this means the fan is not blowing fast enough and any warmer, the fan is blowing too fast. This will work on all units if sized right.

If the unit was sized properly the supply air temp should be 18 to 20 deg. F. colder then the return air. [ return air temp should be taken at the indoor air handler because if your duct work has leaks it will pull hot air from your attic or ceiling giving you a false reading.] Also a properly sized unit will make a temperature difference of 20 deg. F. out side to inside air. [ 90 deg. outside 70 deg. inside. ] I have 20 years field .

Rule of thumb is 20 degree split across evap coil. (between return air and supply air )