Clay,
You have a few options.
From the Backup button in the Projects dialog, you can simply make the project Read-Only. This will back it up, remove it from the project list, and prevent any changes to it. Yet it will still remain in the database, so that you can import items from it, reopen its files, and so on. Should you need to bring it back to read/write status, simply click the Restore button to do so.
Old projects that don't need to be available to import items or ever open old files, can be deleted if desired.
Alternately you can use the Organization tab of the Projects dialog, so that your organization of projects makes it so that it just doesn't get in your way. For instance by organizing projects by client, type, year, etc, so that all previous projects are there, just not in your way.
--J