Coloque la conexión de la base de datos en ServletContextListener

<?xml version="1.0" encoding="UTF-8"?>
<web-app xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://java.sun.com/xml/ns/javaee" xmlns:web="http://java.sun.com/xml/ns/javaee/web-app_2_5.xsd" xsi:schemaLocation="http://java.sun.com/xml/ns/javaee http://java.sun.com/xml/ns/javaee/web-app_2_5.xsd" id="WebApp_ID" version="2.5">
  <display-name>TestServlet</display-name>
  <welcome-file-list>
    <welcome-file>index.html</welcome-file>
    <welcome-file>index.htm</welcome-file>
    <welcome-file>index.jsp</welcome-file>
    <welcome-file>default.html</welcome-file>
    <welcome-file>default.htm</welcome-file>
    <welcome-file>default.jsp</welcome-file>
  </welcome-file-list>
  <listener>
    <listener-class>com.programcreek.testservletlistener.myServletListener</listener-class>
  </listener>
  <context-param>
    <param-name>url</param-name>
    <param-value>jdbc:mysql://localhost/</param-value>
  </context-param>
  <context-param>
  	<param-name>database</param-name>
  	<param-value>testdb</param-value>
  </context-param>
  <context-param>
  	<param-name>user_name</param-name>
  	<param-value>xiaoran</param-value>
  </context-param>
  <context-param>
  	<param-name>password</param-name>
  	<param-value>xiaoran</param-value>
  </context-param>
  <servlet>
    <description></description>
    <display-name>testClass</display-name>
    <servlet-name>testClass</servlet-name>
    <servlet-class>edu.uams.testservlet.testClass</servlet-class>
  </servlet>
  <servlet-mapping>
    <servlet-name>testClass</servlet-name>
    <url-pattern>/testClass</url-pattern>
  </servlet-mapping>
 
</web-app>

package com.programcreek.testservletlistener;
 
import javax.servlet.ServletContext;
import javax.servlet.ServletContextEvent;
import javax.servlet.ServletContextListener;
 
/**
 * Application Lifecycle Listener implementation class myServletListener
 *
 */
public class myServletListener implements ServletContextListener {
 
	/**
     * @see ServletContextListener#contextInitialized(ServletContextEvent)
     */
    public void contextInitialized(ServletContextEvent event) {
 
    	ServletContext sc = event.getServletContext();
 
    	String url = sc.getInitParameter("url");
    	String user_name = sc.getInitParameter("user_name");
    	String password = sc.getInitParameter("password");
    	String database = sc.getInitParameter("database");
    	Database db = new Database(url + database, user_name, password);
    	//System.out.println("in the listener!!");
    	sc.setAttribute("db", db);
 
    }
 
	/**
     * @see ServletContextListener#contextDestroyed(ServletContextEvent)
     */
    public void contextDestroyed(ServletContextEvent arg0) {
        // TODO Auto-generated method stub
    }
 
}

package com.programcreek.testservletlistener;
 
import java.sql.Connection;
import java.sql.DriverManager;
import java.sql.ResultSet;
import java.sql.SQLException;
import java.sql.Statement;
 
public class Database {
 
	private Connection conn = null;
 
	public Database(String url, String user_name, String password) {
		try {
			Class.forName("com.mysql.jdbc.Driver");
 
			this.conn = DriverManager.getConnection(url, user_name, password);
 
		} catch (ClassNotFoundException e) {
			// TODO Auto-generated catch block
			e.printStackTrace();
		} catch (SQLException e) {
			// TODO Auto-generated catch block
			e.printStackTrace();
		}
	}
 
	public Connection getConnection() {
		return this.conn;
	}
 
	public ResultSet runSql(String sql) throws SQLException {
		Statement sta = conn.createStatement();
		return sta.executeQuery(sql);
	}
}

package com.programcreek.testservletlistener;
 
import java.io.IOException;
import java.io.PrintWriter;
import java.sql.Connection;
import java.sql.ResultSet;
import java.sql.SQLException;
import java.sql.Statement;
import javax.servlet.ServletException;
import javax.servlet.http.HttpServlet;
import javax.servlet.http.HttpServletRequest;
import javax.servlet.http.HttpServletResponse;
 
//import javax.servlet.ServletContext;
 
/**
 * Servlet implementation class testClass
 */
public class testClass extends HttpServlet {
	private static final long serialVersionUID = 1L;
 
	/**
	 * @see HttpServlet#doGet(HttpServletRequest request, HttpServletResponse
	 *      response)
	 */
	protected void doGet(HttpServletRequest request,
			HttpServletResponse response) throws ServletException, IOException {
 
		response.setContentType("text/html");
 
		Database db = (Database) getServletContext().getAttribute("db");
		PrintWriter out = response.getWriter();
 
		String sql = "select * from user";
		ResultSet rs;
		try {
			rs = db.runSql(sql);
 
			while(rs.next()){
				out.println(rs.getString("user_name"));
			}
		} catch (SQLException e) {
			// TODO Auto-generated catch block
			e.printStackTrace();
		}
 
	}
 
	/**
	 * @see HttpServlet#doPost(HttpServletRequest request, HttpServletResponse
	 *      response)
	 */
	protected void doPost(HttpServletRequest request,
			HttpServletResponse response) throws ServletException, IOException {
		// TODO Auto-generated method stub
	}
 
}