why do human beings enjoy sex so much more that other creatures like wild and domestic animals?

The only other creatures that are known to have sex just for the fun of it are dolphins. I am not sure why humans and dolphins have sex just for fun. It is kind of odd. I think it is just a built in natural instinct. As for your other question, other animals also have babies that have birth defects. But those babies do not survive long in the wild and that is why you rarely see them..

All other animals enjoy sex or they wouldn't do it.  The difference is that, unlike humans, most animals only have the drive "during" the mating season when the female is receptive and turns the males on.  Some animals, like big cats, can have sex up to 20 times in one day, and each day, when the female is receptive.
Humans are turned on by other things than just the "smell" of the female or the right time of the year.  Vision plays the biggest part in turning on humans and brings on the desire, unlike animals which are mostly scent oriented.  
The biggest problem with human sexual desire is that many people do not THINK before they act, and that is why deformed and unwanted children are born.  That is also why our human population is rising and rising and rising, until someday we will use up all our natural resources and then, through our sheer numbers, we will destroy this beautiful planet called Earth.  And, this will continue to happen, until we believe in and use contraceptives regularly "without" it being claimed some kind of sin, until abortion is legal, and until we understand that more than two children per family is wrong and will only hurt us in the "long run".
Sex is wonderful and there is nothing wrong with it.  We just need to "think" before we do "it", and take the necessary steps to prevent unwanted children from being born.