One of the most common reasons a cucumber will crack and split open on the vine is over watering and / or heavy rain. When cucumbers get too much water the inside will grow at a more accelerated rate than the outside skin can keep up with. The skin then splits.
When the plants are kept somewhat dry, as many gardeners will do when fruit is starting to develop, the fruit skin loses much of its elasticity. A sudden surge of moisture, such as heavy rains or over zealous watering commonly cause long deep cracks on the fruit surface, and at times the cucumber basically bursts open as the innards develop at a rate the skin, lacking elasticity, can not keep up with.
Other problems associated with water issues include Lowered pest and disease resistance, Lower quality cucumbers such as splitting. Blossom End Rot which is caused by irregular and fluctuating moisture, drought and over saturation will reduce calcium uptake into the plant. A lack of calcium leads to Blossom end rot.