I am a mother, so I confess that I'm a little biased about the importance of a mother in a child's life. ;) Nonetheless, fathers play a critical role as well...
For instance, did you know that a father's raucous horseplay with children has a powerful influence on child development? It teaches a child to regulate emotions as they learn to cue in to another's emotional state and when/how to calm down after intense experiences. Of course, there is a healthy and unhealthy way of fathering. A healthy father is in in tune with their child's emotions and limits. A healthy father is also aware of the details in a child's life, such as knowing their friend's names, favorite hobby or toy, etc., which in turn helps him to offer better emotional support and guidance. Here are some other examples from John Gottman, et al's "Raising an Emotionally Intelligent Child."
Effects of a healthy father in a boy's life:
> Boys develop better social skills and peer relationships
> Boys are better able to find balance between masculine assertiveness & self-restraint
Effects of a healthy father in a girl's life:
> Girls will less likely become sexually promiscuous at a younger age
> Girls will more likely develop healthy relationships with men as adults
What kids develop from a healthy fathers' presence in their lives:
> Increased empathy and compassion
> Better social relationships
> Longer, happier marriages
> Having their own kids
> Engaging in healthy recreational activities with nonfamily members
> Better academic success
> Better career satisfaction