Is there any way to help someone who is not a relative or employee
immigrate to the US?  I recently found out that a friend is an illegal
alien and I'd like to sponsor her if possible.  All I saw on the INS
website was information about sponsoring a relative.

If by "friend is an illegal alien" you mean this person is ALREADY in
the United States, and is here illegally (overstayed visitor's visa,
smuggled across border, etc)--this friend is ineligible to apply  for
permanent resident status--and in this post 9/11 world--is very
vulnerable and likely to get into a great deal of trouble if she comes
to the attention of authorities now.  See this section of the US
Citizens and Immigration website:
http://uscis.gov/graphics/howdoi/LPReligibility.htm#k

Consulting an attorney who specializes in immigration matters would be
the best bet- though not inexpensive. Good luck.