Research schools' scholarship programs. Many schools offer merit-based scholarships, in addition to need-based grants or loans. These scholarships may be awarded on the basis of applicants' undergraduate records alone, or on the basis of work experience or interests. For example, Cardozo Law School gives scholarships to its Public Service Scholars, all of whom have demonstrated an interest in serving the public good. Particularly if financial aid is of serious concern to you, or if you will not qualify for much (or any) need-based aid, you should review schools' scholarship offerings before you apply and see if you may be eligible.
Apply to schools to which you are overqualified. If you are applying to schools that offer merit scholarships, you will obviously be more likely to receive these if you are at the top of the applicant pool. Similarly, try to find schools that offer scholarships in other fields (public service, for example) for which are you are qualified.
Negotiate with schools. If you don't apply early decision, you may be able to negotiate your financial aid package, particularly if you have multiple offers. For example, if school X offers you a scholarship but school Y doesn't, you may go back to school Y and see what they can do.
Apply for outside scholarships. If you are a minority, there are more scholarships for which you are eligible, but a few exist that are open to students of varying backgrounds (see the first two links below in Resources). There are also many scholarship databases online, such as Fast Web (the link is also below).