As always, when hunting for a new extension, it's best to start at the Joomla Extensions Directory. There is a Directory category and this includes two listings that have been around the Joomla world for a long time.
SobiPro comes with a solid set of features for free and additional features are available as part of a membership subscription. You can customize the data fields which means a truly flexible solution. And, as with all these solutions, this also means that you are not limited to a business directory. These extensions can be used for all sorts of listings.
Mosets Tree is another contender and it was the initial choice to power the Joomla Extensions Directory (I think this is still the case - can anyone confirm?). This one is commercial only, but certainly worth a look.
Another option is to use a dedicated content construction kit (CCK) such as K2 or Zoo. In the case of the latter, there is an option to buy an application pack, which includes a pre-built business directory. The design is terrific and you can add or remove your own fields.
There are three options to consider for your Joomla powered business directory.
Have you used one of these? Got another solution? Tell us about it below.