In reality, blue skies have many more colors in them than a couple of tubes of blue paint. Of course there are all the other colors on a cloudy day, dawn or sunset. But what they all have in common is the combination of all three primaries.
Of course, the blue sky has more blue than red or yellow. Skies are usually painted darker and cooler at the top. At the horizon the sky picks up more warm, earth colors and are lighter in value. Blue skies should have other colors in them, red, yellow, orange, green). Never use just blue and white.
I usually introduce some of the other colors in my painting into the sky. It helps to integrate the painting. Be careful with the values. If you introduce a different color in a darker value you can have a muddy look. The values have to be the same. Also, be careful not to get the sky too blue. If your sky is too light, it won't have any rich, wonderful colors. If it is too dark, it may be the most important color in your painting.
Remember that your sky is your source of light. In most instances the sky is the lightest part of your painting. So, what are the blues that you should use? Any blue that goes with the rest of your painting! Ultramarine has a bit of a violet to it. I use it more often in the top part of a sky. The bottom of the sky should be a lighter blue, cerulean, turquoise, thalo or prussian.
I always add some yellow and cadmium red throughout the sky with a cooler alizarine in the top part. Cobalt I reserve for bright blue skies that I want to stand out. Violets and thalo or cobalt turquoise together can also be exciting. Mix it up! Don't stick to the same ol' thing. Have fun and see how exciting your skies can be.