In what organism is the male one inch long, but the female can be up
to 2 meters long?

Thanks for a very intriguing question.

The phenomenon you are referring to -- where the males and females of
a species are dramatically different in appearance -- is known in
biological circles as sexual dimorphism.  A Google search on [
"extreme sexual dimorphism" size ] led to an article on an odd
creature called the blanket octopus, which seems to be the animal
you're looking for.

http://www.rsnz.govt.nz/publish/nzjmfr/2002/061.pdf

First encounter with a live male blanket octopus:
the world’s most sexually size-dimorphic large animal

"Our observation...of a living male...off the northern 
Great Barrier Reef, Australia...  The animal approached dive lights at
c. 8 m deep. It is 2.4 cm [note: one inch] in total length and weighs
0.25 g. It is mature with a fully developed testis and reproductive
tract....
By contrast, females...attain sizes of up to 2 m long (Nesis 1987)."

So there you have it -- a one inch male and a 2 meter female.  

I had actually expected the answer to be the anglerfish, an oddball
staple of public television nature documentaries.  The male of some
anglerfish species is not only tiny, but a parasite to boot:

divermag.com/archives/nov2000/fish-nov00.html

"...nowhere is mating more bizarre than in the case of some deep water
anglerfish. The tiny male, only about one and a half inches long,
latches on to the much larger female which can be up to 45 inches
long, and over time his body becomes a fixed appendage of hers, a mere
sperm producing organ of the female."

So this creature, too, almost -- but not quite -- meets your size
criteria.  And I can't resist closing with this quote from a one Dr.
Caruso, one of the world's leading authorities on anglerfish:

oceanexplorer.noaa.gov/explorations/ islands01/log/sep25/sep25.html

"The male is parasitic, and essentially nothing more than a
self-propelled pair of gonads directed by a nose."

Whew...makes me glad to belong to good old homo sapiens.  

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