As long as you don't move it, or cause it to move abruptly while spinning, you should be okay. It's easier to cause damage from a vertically mounted/placed hdd than a horizontally mounted/placed hdd because of centrifugal force...the disk platter doesn't want to move while spinning at high speeds, while you are forcing the enclosure to move. This will cause microscopic scratches that leads to errors and irreversible damage. Good HDD's now-a-days come with very fast reacting vibration sensors that park the head(s) of the drive upon vibrations. A very loose example of this is placing an XBOX 360 vertically, and jiggling it...you know what happens
Though, the hdd's platter is MUCH MUCHHHH more tightly attached to the bearing assembly that allows it to spin, the force from it spinning actually allows the disk platter to ever so slightly bend when placed vertically. This kind of vibration is near eliminated by placing it horizontally.
With that said, half of all my hdd's are placed vertically.