I currently have an external hard drive where I've misplaced the power
adapter.  As with everyone, I have a house FULL of old power bricks. 
In researching, the previous models was REGULATED.

How can I tell which power adapters I have are Regulated or Un-Regulated.  

I wish to do no harm to my device but I don't wish to purchase a
replacement.  I already have three similar power bricks with identical
specifications.  Please let me know.  Thank you.

The usual wal-wart transformer, that is the one that directly plugs
into an outlet, is usually unregulated.

The ones that have a rectangular box with two wires heading out: one
for the outlet and the other to the device is practically always
regulated.

If it looks like a wal-wart or any other kind but it specifice a broad
rangle of voltages, say 100-240 V then it is regulated.

Any power supply that matches the voltage and the plug polarity, and
meets or exceeds the current rating can be used.

However, unregulated power adapters can suffer from varying voltage. 
In situations, couldn't an unregulated AC/DC adapter's output
fluctuate from a standard 12V to an unsafe 16-18V (thus causing damage
to an electronic device which was designed for a regulated power
supply).

Ive seen very few power bricks or cubes that were regulated, with or
without a cord to the ac outlet. I have one that is likely partially
regulated as it produces 14 volts at very light or no load and 12.6
volts at 5 amps, which is likely the design current. About 11 volts at
9 amps, which is likely overload and will lead to failure of the
brick, if loaded that heavy for more than a minute. I've had good
success using power cubes that are almost right, but, I would not risk
a $100 hard drive that specifies a regulated power brick.   Neil

Hi  frozenrubber,

"If an adapter doesn't have "regulated" printed on its label, you
can't be sure about it without testing it. Testing's really easy,
though; get yourself a $15 multimeter, set it to an appropriate DC
volts range, plug the adapter in, and apply the probes to the plug
terminals. That'll give you the unloaded voltage. If it's
significantly higher than the rating, you've got an unregulated
plugpack."
http://www.dansdata.com/danletters049.htm

Regards,
hummer