Although undocumented and DACA-mented students are currently ineligible to receive federal financial aid, there are a number of scholarships which do not require active Social Security Numbers in their application processes. There are also a handful of scholarships targeted towards undocumented youth.
The Mexican American Legal Defense and Education Fund (MALDEF) has compiled a very useful list of such scholarships, which can be accessed here.
A similar resource has been put together by the National Immigration Youth Alliance (NIYA).
As of Fall 2013, the following states have passed versions of the DREAM Act, which by and large allow undocumented students to access in-state tuition rates and state financial aid: Texas, California, Illinois, Utah, Nebraska, Kansas, New Mexico, New York, Washington, Wisconsin, Massachusetts, and Maryland.