You sure can... you can configure using asp with an ISAPI extension, as long as you're using Apache on a Windows NT, 2k, or XP box. You'd have to set up mySQL as an ODBC datasource to use it within ASP, which would then be just like using any other OLE datasource except for a few differences in the connection string.
Do note that support will be a pain -- using the ISAPI filters with Apache to use ASP is something that really doesn't make sense -- if you have Windows 2k or XP, you already have IIS, and then Apache seems silly. If you're not on Windows, you'd have to look at using a Chillisoft product to provide ASP engines.
As the previous poster mentioned, it's worth looking at php if you're going to use mySQL and Apache, especially if the price of 2k or XP is what's keeping you from using IIS or if you're not on Windows (the price of learning php <<< price of Chillisoft). Tutorials abound. I'd suggest using Postgresql instead of mysql (function over speed), but that's just me.
Ruffin Bailey