After your aquarium has been set up for a few months/years you tend to get used to the water chemistry. You normally know what your nitrate level will be like at the end of the week. However, weekly water tests won't hurt at all. I don't think there is any need to do it every day in a mature aquarium. In a lot of cases, your fish will tell you if the water isn't quite right. Laboured breathing, hanging at the surface, sign of disease etc. If you add fish, a specially large fish, then its always a good idea to test the water more regularly for the first week or two.
If you want to check your water after each change, by all means do so. It will certainly tell you how much you have reduced the nitrate by. It will also tell you if you've upset the biological filter at all, if this happens, you will notice the ammonia nitrite readings.