I've had to do this for a couple of articles I've written recently, and I thought I'd pass along pointers to some useful databases. They are generally for-pay databases, but my sense is that most universities have subscriptions to them. If you're on a law review editorial board, you might want to make sure that your cite-checkers know about these, since they can save the cite-checkers a good deal of effort. All of the databases are full-text searchable and at the same time provide images of the original pages, so you can be sure that you're not falling victim to a transcription error.
1. Pre-1700 English books (not just on law): Chadwyck-Healey's Early English Books Online (EEBO).
2. 1700s English books (not just on law, plus some from outside England): Gale's Eighteenth Century Collections Online.
3. 1700s and 1800s American books and pamphlets (not just on law), plus newspapers (which sometimes reported otherwise unreported legal decisions, jury charges, and the like): Readex's Archive of Americana.
4. 1800s and early 1900s English and American legal treatises and other law books: Gale's Making of Modern Law (if you have a subscription, it should be available through your library Web site).
5. More 1800s and early 1900s American legal treatises and other law books: HeinOnline's Legal Classics database.
6. Some reports of English and American trials and other legal documents from the 1600s to the early 1900s: Galenet's Making of Modern Law - Trials.
7. English reported court cases from 1220-1865 (whether cited to Eng. Rep. or to the individual reporters): HeinOnline's English Reports database.
8. Some other pre-mid-1600s English cases (for instance, from Star Chamber): John Rushworth, Historical Collections of Private Passages of State, Weighty Matters in Law, Remarkable Proceedings in Five Parliaments 59-60 (London, Robert Boulter 1680), available on Early English Books Online (see 1 above).
9. Some early books: Google Books. [Thanks to commenter cd for reminding me about this item, which I have used in my research but neglected to include in this post at first.]
10. Of course, Westlaw and Lexis, which contain nearly all published American court cases.
11. Your library bookshelves, which likely contain a few volumes with cases that aren't on Westlaw and Lexis (such as the New York City-Hall Record, Wright's Ohio Reports, and the like.
12. Your library's online catalog, which may give you online access to many old sources, either through your own library or other cooperating libraries.
If you have other suggestions, please post them in the comments.