The white spots on the squash leaves are almost certainly powdery mildew. Powdery mildew is a fungus and squash plants are very susceptible to infection. It can also spread very easily between plants and you can see that it is already starting to spread to neighboring plants. It begins by producing very characteristic powdery circular spots on the leaves. These spots grow larger and will eventually cover the whole leaf causing it to turn yellow. The fungus may also spread to other parts of the plants such as the stems, flowers or fruit.
The best way to prevent powdery mildew is really to take the necessary precautions to prevent it emerging in the first place. Make sure that you plant your squash in full sun and don't overcrowd them. This ensures maximum air circulation around the plant and allows plants to dry quicker when they get wet. A protective fungicide may be required for squash as it is particularly susceptible. Sulfur can be used on leaves to prevent the emergence of powdery mildew. There are many forms available but wettable sulfur is generally considered to give the best control.
If, as in your case, powdery mildew has already appeared then you will need to treat it with either an horticultural oil or an organic, plant-based oil such as neem oil. This will kill off existing fungi and should be applied as soon as powdery mildew symptoms are observed. Fungicides can be damaging to your plants if used incorrectly so always be sure to read the instructions on the label before applying any fungicide, organic or otherwise, to your plants.
Finally, In the case of your zucchini plant I am inclined to think that the plant is not diseased and it is in fact simply a natural pattern on the leaves. Many zucchini varieties produce mottled leaves. If you look closely, you will see that the patterning is very regular and almost symmetrical. If this was a disease such as cucumber mosaic then the leaf symptoms would be blotchy and irregular.
I don't think you have anything to worry about this year. Space your plants well to encourage good air circulation and do not over water. Powdery mildew will thrive in wet soil and high humidity. Look out for the patterned leaves on the zucchini again of you grow the same variety, that should reassure you that its natural.