Being an independent student means that your aid is calculated only on your income and assets. In most cases, independent students make far, far less than their parents, so in theory you should experience an increase in financial aid.
Keep in mind, however, that the federal government still calculates a higher percentage of the student's income toward student contribution than parents' income toward family contribution. Also, if you have siblings attending college, you no longer benefit from their enrollment. If you have three kids in your family attending college, all using your parents' income for student aid basis, once you're independent you're on your own. No increase in aid will come from the additional family members enrolled in college.
In addition, your credit history is the one used to calculate any private loans--not your parents' credit history. While most students have good credit (largely because they haven't had enough money to HAVE a credit history), if you have credit problems in your past, remember that it might affect you negatively as you go for independent student financial aid.