There are colleges which, will classify themselves as need-blind meaning, their admissions process does not take financial standing, ie., need, into consideration. Although this sounds encouraging please keep in mind that if a student "in need" is accepted , colleges are not obligated, to provide full aid in order to ensure they will be able to attend. In other words, many schools want to know that if they offer you acceptance, you can afford their cost allowing them to count on yet another student joining their ranks. There are many, many need-blind schools but sometimes much as I hate to say it yes, financial need can impact your application. You will need to do some research on each of your schools in regard to what a general financial aid package looks like and then, compare a general package to your needs and the financial standing of your family in order to determine if you should be applying to a particular school or, if you need to be looking at another. Please see the article below for a more detailed response:
"Need-blind admission is a term used in the United States denoting a college admission policy in which the admitting institution does not consider an applicant's financial situation when deciding admission. Generally, an increase in students admitted under a need-blind policy and needing financial aid requires the institution to back the policy with an ample endowment or source of funding. Being need-blind is a statutory requirement for institutions to participate in an anti-trust exemption granted by Congress which remains in effect until September 30, 2015. An institution may be need-blind in any given year by policy (de jure) or by circumstances (de facto).
Most colleges and universities cannot afford to offer financial aid to all admitted students and many will admit all students on a need blind basis but cannot offer them sufficient aid to meet need. Many schools who admit all U.S. citizens or resident aliens without regard to need do not extend this policy to international students or to transfer students. Therefore schools, especially private ones, which are need-blind and full-need for all applicants, including internationals, tend to be much more selective as they have relatively more applicants than other similar schools.
Need-blind admission does not necessarily mean a "full-need" financial aid policy—where the school agrees to meet the full demonstrated financial need of all its admitted students. Indeed, the two policies can be in tension because need-blind admissions and full-need financial aid together commit the school to spend an undetermined amount of money regardless of other budgetary constraints. Thus, some need-blind schools will admit students who will nonetheless not be able to attend because of deficient financial aid awards.
"Institutions self-define their definition of meeting full demonstrated need. There is no U.S. standard that an institution must abide by to claim that they meet fully demonstrated need. Therefore, an applicant's financial aid package can vary significantly at various schools, even if all of these institutions claim to meet fully demonstrated need." Wikipedia