"I have created the alerts in my moss site and I received the First Initial Alert Notification Mail After that I have not received Any mails from the Library if any changes on it".

I have done the following steps for fixing this issue.
 
1. Confirm the account running the SharePoint Timer service is the account which has the administrator Full Control permission over the site and the full permission over the content database. If Not provide the permission in the site and the content DB of the site.
 
2. Confirm your site has the correct default zone URL and the URL is working perfectly(because in my case, i have changed my default zone url from to http://dotnetix.com/ in the central Admin after that the sharepoint not able to recognize the new url due to hostheader and not added in the host name  in the host file)
 
3.Then Run the folllowing stsadm Commands.
    a. stsadm.exe -o setproperty -url http://dotnetix.com/ -pn alerts-enabled -pv true
    b. stsadm.exe -o setproperty -url http://dotnetix.com/ -pn job-immediate-alerts
 
Now the Alerts in moss should work.