If you are using a topology with a single web server and an MSDE or SQL Server database on the same machine then you must give the "NT Authority\System" account that the Reminder Service is running under Full Control permission for any Web Applications you intend to use the Reminder Web Parts in.

Note - If you chose to "Automatically set permissions" during installation then these steps have already been performed for you.

You can do this by using the following STSADM command :-

stsadm -o addpermissionpolicy -url http://<yoururl>-userlogin "NT Authority\System" -permissionlevel "Full Control"

(Remember to repeat the command for each web application you are running)

Alternatively you can add the permissions using SharePoint Central Administration > Application Management > Policy for Web Application

If at a later date you add a new web application you will need to add the Full Control permission for NT Authority\System

Note - if you are using SQL Server then by default the NT AUTHORITY\System account is given the sysadmin role which will give the Reminder Service the required permissions to access the database. If this has been removed then you will have to setup a local or domain account for the Reminder Service and give it it permissions described here.