The user running the SharePoint performance monitor application (logged in account) will need to have at least 'View Only' access to the SharePoint Web Site that will be monitored by SharePoint performance monitor.
In order for SharePoint performance monitor to monitor counters on the target server, the logged in account will need WMI rights. The easiest way to ensure that the logged in account has these rights is to add it to the Administrators Local Group on the monitored server.
For additional information regarding WMI and alternative ways to assign rights to a remote machine, please review the following Microsoft article:
http://www.microsoft.com/technet/scriptcenter/topics/help/wmi.mspx#E2C