Bloomberg is the best source to begin your docket research. It provides free access to PACER (federal district court and appellate court dockets), plus selective state court docket coverage. (Don't have an account? See the Password FAQ.)
Bloomberg Law's docket search features are continually evolving, so please stop by the Reference Desk to talk with a law librarian about your docket research. Current advanced features include searching federal district court cases by both Nature of Suit and by Cause of Action (statute), customized docket search alerts, and docket update alerts.