Should database files be on different disk(s) than OS?
It's typically good practice to seperate your OS installation from your database installation to isolate OS disk issues from database disk issues.

The primary reason for this is to reduce the change that a problem with the OS could prevent recovery of the database, or vice versa.  If your database fills up the free disk space, it can crash both the database and the OS.

This also allows you to have different recovery options available for the different pieces.  We typically run RAID 1 (Mirroring) on our OS disks, and RAID 5 (or some other type of parity + striping) on our Database disks.  Since the OS disk has fewer writes, we can take the performance hit of mirroring, to reduce recovery time in a crash situation.  But on the Database side we want to maximize the performance of reads/writes at the expense of recovery time in a crash situation.