Sometimes Sharepoint and Project are installed with a AD User instead of a system account and it happens that the password for the user expires after X days due to a AD Policy.

The best way to avoid this is to follow the following Technet article:

Plan for administrative and service accounts SharePoint Server

http://technet.microsoft.com/en-us/library/cc263445.aspx

Change passwords used in administration accounts Project Server

http://technet.microsoft.com/en-us/library/cc197684(v=office.12).aspx

However if you run into this issue this is where i've have refreshed the password in order to make the environment working again:

  • Changed the password for the SharePoint and Project Services
  • Changed the password for the Application pools (advanced-identity)
  • In the central administration - Service Accounts- credentials Management we registered the account again for the web application
  • Restarted the Project Application Service from the Central administration - manage services on farm- and we got a error related to the password for the account. 
  • Executed in PowerShell the following command to update the credentials: Set-SPManagedAccount -UseExistingPassword
  • Restarted the Project Timer and Queue Services.

  • Now Sharepoint and Project should work again.

If you don't want to change the System account at the Farm level you could exclude the user from the password change and implement one at the Sharepoint level:
http://technet.microsoft.com/en-us/library/ff724280.aspx