If it's really simple, you can use the CSV viewer from Github, which has a built-in search tool.
A similar tool is datapipes and for HTML from OKFN Labs. See the demo.
For a more complicated dataset, with more than one table, then another simple option is to export the database as a .SQL file and then let users import it into the SQL database of their choice. You can host the .sql file anywhere, but Github and Datahub.io are two good choices. Here is a simple example.
I can expand this answer for tips on how to do this if that is the direction you go.