<p>Yes, colleges that do not do this are called "need blind". </p>
<p>There are really two components to the question. A college that is need-blind will not let your financial situation affect their admissions decision, but they may not fulfill your need. On the other hand, a college may not be need-blind but they may guarantee all students who are actually accepted enough finan aid to actually attend. According to this website, there are only 28 colleges that are both need-blind and will guarantee the finan aid.
<a href="http://www.wfu.edu/admissions/finaid/twenty-eight.html%5B/url%5D">http://www.wfu.edu/admissions/finaid/twenty-eight.html</a></p>
<p>However, the fact that a college isn't on this list doesn't mean that they are stingy. Harvard isn't on the list. They may just not want to make a total committment in all cases.</p>