Brad Abrams has demonstrated that with just a few lines of code a developer can add auto-completion to an ASP.NET website. He does this with an otherwise standard search box.
His example relies on the AutoCompleteExtender, which is available as part of the ASP.NET AJAX Extensions. To avoid explicit database logic, an entry is added to the profile section of the web.config file. This shifts the burden to the Profile Provider.
The default Profile Provider for ASP.NET uses SQL Server as a backing store. Of course, you can create your own profile provider if you need to.