I saw a post recently that asked about backing up the Resource database. The person said they just realized that it wasn't included in their backup scheme and was worried.\
Don't worry, you don't need to back it up.
The page at MSDN describes the Resource database as essentially a large lookup table(s) for the SQL Server itself. It can find the system objects that are used: tables, views, DMVs, DMFs, etc. When the server is upgraded, a new copy of the Resource database is copied over. The objects don't have to be built from scripts with DROPs and CREATEs.
This means, however, that each time you patch your server, you potentially could be copying over a new version here if some system object changes. That means that you don't really want to back up this database.
If you are restoring to a new server, when you install that server, it will have the correct copy of the Resource database for your system. If you were to copy over an incorrect version, the system objects might not match up with the system code in the SQL Server executables and DLLs. That would be bad.
I haven't seen notes about the Resource database becoming corrupted, but it could. In that case, I'd suggest you copy the files from another SQL Server of the same version, or install SQL to another machine, patch it up, and then copy the files to your damaged installation. That could be a problem, but it does mean one other thing.
You ought to be tracking your SQL Server version and build on a regular basis as part of your monitoring.