Place this function within reach of any page you wish to use the mySQL() function on. Example: application.cfm

<cffunction name="mySQL" description="Connects to a mySQL server. No DNS needed">
     <cfargument name="JDBC_URL" required="yes" hint="JDBC URL of the mySQL server to connect to. With or without the leading 'jdbc:mysql://'">
     <cfargument name="username" required="yes" hint="mySQL username">
     <cfargument name="password" required="yes" hint="mySQL password">
     <cfargument name="sql" required="yes" hint="SQL to process">
     <cfargument name="queryName" default="mysql" hint="Name of the query results (optional); Defaulted to 'mysql'">
     <cfargument name="driver" default="org.gjt.mm.mysql.Driver" hint="Driver to use when connecting to server (optional)">

     <cfscript>
          class = createObject("java", "java.lang.Class");
          class.forName(driver);
          dm = createObject("java","java.sql.DriverManager");
          con = dm.getConnection("#iif(JDBC_URL contains 'jdbc:mysql://',de(JDBC_URL),de('jdbc:mysql://'&JDBC_URL))#","#username#","#password#");
          st = con.createStatement();
          resultSet = st.executeQuery(sql);
          "#queryName#" = CreateObject("java", "coldfusion.sql.QueryTable").init(resultSet);
          resultSet.close(); st.close(); con.close();
          return "#queryName#";
     </cfscript>
</cffunction>

All you need to do is run mySQL() wherever you would usually need a query variable.
Example:

<!--- mySQL('path_to_database','username','password','sql'[,'query_name'][,'driver'] --->

There are two easy ways to utilize mySQL().

Both ways have the same effect.