The short answer is yes, there is such a database. EBSCO Publishing has created the NoveList database that is geared directly toward fiction-lovers looking for the next great book. Access to the database isn't free, and it's available only to institutions. Check out your local library's online databases — you may already have free access to NoveList with just your library card!
You can find out more about NoveList at www.ebscohost.com. If your library doesn't subscribe to NoveList, find out how to request it.
Even if you don't have access to this type of database, other resources are available. Ask your reference librarian for help. Different types of book lists have come and gone, so there's no telling what your local reference section might hold. At the very least, your library likely has a copy or two of Genreflecting, which contains information about different genres of fiction and recommended reading lists. And don't forget online library catalogs (for your library or others), which can make searching for the right book easier just by leaving behind all of the other non-book twaddle that turns up in simple Internet searches.
Also, with the soaring popularity of free blogs, personal Web sites, and social networking sites, literally millions of people offer their opinions about great books of all stripes for free online. An Internet search for "best books" followed by practically any other word or phrase — a city or state name, an author's name, a genre, even a particular type of crime — will turn up all sorts of ideas, both good and bad.
If you want a low-tech solution, a number of avid readers have published their own collections of favorite novels. One popular author of such books is Nancy Pearl, whose publications include two volumes of Now Read This; Book Lust: Recommended Reading for Every Mood, Moment, and Reason; More Book Lust; and Book Crush (for kids and teens). Look for them at your bookstore or library.