If you need to delete a Team System Project you need to do it through a command line utility that is installed with Team Explorer. In my case, I created a test project but wanted to also test project deletion. There is no way to delete a project from Team System except through the command line tool, TFSDeleteProject.exe. This utility is in the c:program filesMicrosoft Visual Studio 8Common7IDE folder by default. To delete a project, use the following syntax:

TFSDeleteProject /server:ServerName ProjectName

Optionally, you can use /force to force the removal even if some pieces are locked, but this is not recommended except as a last resort since any locked components would likely be left behind and unremovable.

In my case, running this command resulted in the following output:

Are you sure (y/n)?
Deleting from Build… Done
Deleting from Work Item Tracking… Done
Deleting from Version Control… Done
Deleting Report Server files… Done
Deleting SharePoint site… Done
Deleting Team Foundation Core… Done