I have low a low voltage MR16 track lighting syetem in my kitchen.  In
case you are curioius, the track heads are WAC series 809.

http://www.waclighting.com/USA/products/?categoryid=3&productid=13

In order to save money on electricity, I purchased a single LED MR16
bulb to test.  I found it satisfactory, and decided to order more to
install in the rest of the heads.  My mistake is that I ordered a
different bulb, and when plugging it in, the light is extremely dim
with the new bulbs.  Here are my observations.  The new bulbs that
don't work with the WAC fixtures, are very bright when hooked up to a
DC 12 volt power source. When measuring the voltage of the socket, it
seemed to be at about 8 volts with no bulb plugged in.  The heads are
rated at 12 volts, but all normal halogen bulbs that are plugged in
seem to emit an appropriate normal amount of light.  The same symptoms
are observed on all 6 heads, and 6 bulbs that I have.

Most importantly, please help me to understand why these bulbs emit
such low light, and I would also be interested in hearing any
recommendations for high light output LED MR16 bulbs that would be
compatible with the WAC track lighting system that is referenced
above.

What was the different bulb that you purchased?

The new bulbs you bought are for 12V DC while the track lights are 12V
AC.  Most LED products run reliably on DC.  There are some that run on
12V AC, but they don't last as long, and you need to specify it as a
an AC bulb when you purchase it.  Aside note, this is all assuming the
WAC Track head runs on an Magnetic Transformer, if not and it runs on
Electronic, very few LED MR16 will work long-term.  Electronic
transformer are lighter in weight than Magnetic.