Why is my cucumber fat on one end and skinny on the other?

This could be caused by a few things:  improper pollination, hot temperatures, or too much fertilizer. 

The female flowers need to be completely pollinated in order to form a fully developed cucumber.  The lack of complete pollination leads to only one end of the cucumber becoming fully developed.  The end of your cucumber that looks normal received enough pollen, while the end that looks deformed did not.  If you have low pollinator activity around your cucumber plants, and you are getting a bunch of deformed cucumbers, you may need to resort to hand pollinating the female flower. 

Very warm temperatures can kill pollen, leaving it practically sterile.  Also, a lack of water during hot, dry conditions can cause the fruit to form in a peculiar shape.  Too much nitrogen-based fertilizers can also result in deformed cucumbers. 

You can read more about the causes of misshapen cucumbers here.  If you are still stumped, you may want to check with your local extension office.  Hope this is helpful!  - Gardening Gal