This is an important question. There are many potential problems and risks with networking. Let me name some of the most commons.
First, there are hackers out there that can infiltrate networks through sophisticated programs. You can even go online to see how it is done! This shows you that any person with some know how can infiltrate modest security measures. The professional hacker can do more and even break into large corporations and even governments.
Second, when there is a breech, this is extra problematic for networks, because networks do not merely have one computer, but many computers. So, if a hacker sends a virus, the he or she can bring down a whole network. Of he or she can steal information from many computers. In light of this, the Internet is not as secure as people think it is.
There also also what hackers call IP address attacks or spoofing, which can imitate another person's IP address or conceal it. Through this an hacker can impersonate someone else.