The safest thing is to identify the model and manufacturer of the hard drive and check the drive maker's web site for mounting specifications. There used to be warnings about mounting drives in certain orientations, but I doubt that problem exists for most of today's drives. It never hurts to check.
Here's the FAQ for Western Digitals SATA drives:
"Mount the drive in the system:
The drive can be mounted in a standard 3.5" device bay. The drive can be mounted sideways, on end, or even upside down as long as the mounting screws are used properly. Use either the four bottom screws or four of the side mounting screws to support the drive. This will prevent vibration and provide additional electrical grounding."
A quick look at the specs for a Seagate Cheetah 10K SCSI drive shows mounting as:
"Vertical, horizontal, or top down mounting"