Apart from the fact that all men, both U.S. Citizens and non-citizen men living in the United States, between the ages of 18 and 26 are required to register, NOT registering can cause a delay in your naturalization process!
In most cases, males register within 30 days of their 18th birthday... you can file online at the Selective Service website.
The problems I typically see arise when a foreign national between the ages of 18 and 26 gets his Green Card, and then doesn't register with Selective Service. Some time later, he decides he wants to naturalize, and at that point, if he's over 26 years old (but younger than 31 years old) he'll find that he can be denied due to his failure to register... and he'll have wasted the application fee. Recently, I had to tell a 27-year-old Permanent Resident that we couldn't file an N-400 application for him at present, as he hadn't registered... and by now, it was too late to register.
So, if you are a man between the ages of 18 and 26 and you haven't yet done so -- Register!
(As always, there are some exceptions to this, so be sure to bring your specific situation to an immigration lawyer!)