a) var checkNum = /^[A-Za-z0-9]+$/;
b) var re=new RegExp(“["+s1+"]“,”g”);

a) 用户密码：/^[a-zA-Z][a-zA-Z0-9_]{5,20}$/
b) 邮件:/^[\w-]+(\.[\w-]+)*@[\w-]+(\.[\w-]+)+$/
c) 手机:/^[\d]{5,20}$/
d) 其它常用验证:请百度

!DOCTYPE html>
html>
head>
  meta charset="UTF-8">
  title>jquery ajax/title>
  script type="text/javascript" src="public/js/jquery-2.2.3.min.js">/script>
/head>
body>
form action="">
  label>用户名：/label>span id="check_username">检测/span>
  input type="text" id="t_username" placeholder="请输入"/>
  hr/>
  label>邮箱：/label>span id="check_email">检测/span>
  input type="text" id="t_email" placeholder="请输入"/>
  hr/>
  label>手机：/label>span id="check_phone">检测/span>
  input type="text" id="t_phone" placeholder="请输入"/>
  hr/>
/form>
/body>
script>
  $(function () {
    // 用户名
    $("#check_username").click(function(){
      var str = $("#t_username").val();
      var ret = /^[a-zA-Z][a-zA-Z0-9_]{5,20}$/;
      if(ret.test(str)){
        alert('ok');
      }else{
        alert('wrong');
      }
    });
    // 邮件
    $("#check_email").click(function(){
      var str = $("#t_email").val();
      var ret = /^[\w-]+(\.[\w-]+)*@[\w-]+(\.[\w-]+)+$/;
      if(ret.test(str)){
        alert('ok');
      }else{
        alert('wrong');
      }
    });
    // 手机
    $("#check_phone").click(function(){
      var str = $("#t_phone").val();
      var ret = /^[\d]{5,20}$/;
      if(ret.test(str)){
        alert('ok');
      }else{
        alert('wrong');
      }
    });
  });
/script>
/html>