I want to know what the difference between a democracy and a republic
is. Can you have a democracy with out a republic? More specifically I
would like to know what the criteria is for judging whether or not a
country is a democracy.

Hi! Thanks for the very interesting question.

In our present time such terms are used interchangeably but the
original meanings were indeed different.

DEMOCRACY:
"Democracy: The word democracy stems from the Greek words demos,
"people" and kratos, 'rule.' A democracy is simply a system of
government in which the people rule."

"In the earliest democracies and even at the time the Federalist
papers were written in the late 1780s, the term democracy implied a
government in which the people assembled and expressed their
individual vote on issues facing the community as a whole. ." (1, 2,
3, 4, 5) This approach to democracy would be described today as
'direct democracy' and is distinct from the 'representative democracy'
system crafted by our founding fathers in which the people elect
individuals to represent them - the system that remains in place today
in the United States."

REPUBLIC:
"Republic: The term republic today refers to a system of government in
which the people rule, but do so through the popular election of
representatives who in turn make the laws. The difference between a
republic and a democracy has become indistinct over the centuries, and
today we tend to use the terms interchangeably. The terms "Direct
Democracy" or "Pure Democracy" (see above) have become today the
necessary terms to specify that a direct vote by the electorate is
involved."

"Glossary & Definitions"
http://www.afrd.org/glossary.htm

So in this case, we can see that most countries like the US which call
themselves as democracies are actually republics.

"Notice that in a Democracy, the sovereignty is in the whole body of
the free citizens. The sovereignty is not divided to smaller units
such as individual citizens. To solve a problem, only the whole body
politic is authorized to act. Also, being citizens, individuals have
duties and obligations to the government. The government's only
obligations to the citizens are those legislatively pre-defined for it
by the whole body politic."

"In a Republic, the sovereignty resides in the people themselves,
whether one or many. In a Republic, one may act on his own or through
his representatives as he chooses to solve a problem. Further, the
people have no obligation to the government; instead, the government
being hired by the people, is obliged to its owner, the people."

"REPUBLIC vs. DEMOCRACY"
http://www.chrononhotonthologos.com/lawnotes/repvsdem.htm  

In a particular country, the following criteria must be met before it
could be considered a democracy:

1. Effective Participation
2. Voting Equality
3. Enlightened Understanding
4. Control of the Agenda
5. Inclusion

An explanation of each criteria is available in our next link.

"What is a Democracy?"
http://www.couplescompany.com/Features/Politics/Structure1.htm

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Easterangel-ga          
Google Answers Researcher

Good response to my question. Provided the distinction I was looking for.

The monarchies in Western Europe aren’t republics, but can't be
defined as anything but democracies, (since they have a king [without
real power], instead of a president).

Perhaps easterangel should clarify that?

"...in a democracy, the people meet and exercise the government in
person; in a republic, they assemble and administer it by their
representatives and agents." Federalist No. 14 by James Madison,
Friday, November 30, 1787

Carter: You just gave an example of bad logic by typing the monarchies
of Western Europe HAVE to be democracies as they are not republics. 
Clearly they can be something else as is the UN, WTO, GATT, NATO and
Roman Catholic Church. Only small clubs can meet all the criteria of a
Democracy as easterangel defined it, and I thought that was a
reasonable definition. The ability of any citizen to set the agenda,
could clearly lead to chaos (gridlock?) unless tempered by some
restrictions. Every large group needs an executive group of some sort,
but I don't think a president is nesessary for a representative form
of goverment.  Neil

neilzero:

Carter? I assume you meant me.

I didn't say they were democracies just because they weren't
republics. I said they were NOT republics BUT democracies, which is
something different, it's not a "A and not B gives C" statement, but
rather "A and not B but C, gives C doesn't (always) imply B" the later
can, mistakenly, be read between the lines of Easterangel's answer,
which is why I thought he/she should clarify that.

Easterangel's statement:

"So in this case, we can see that most countries like the US which
call themselves as democracies are actually republics."

Might not be true, or I think at least the system of democratic
monarchies in for example Spain and UK should be mentioned as well,
which is why I wrote the comment above, I don't mean that the answer
isn't good, just that I think it deserves a little clarification.

American politicians have proved to be ignorant when it comes to this:

CNN Europe 18th February 2003:
“The U.S. president's brother Jeb Bush has sparked criticism after
mistakenly referring to Spain as a republic in a speech to Spanish
business leaders during a trip to Madrid to discuss business
opportunities.”

http://edition.cnn.com/2003/WORLD/europe/02/17/jebbush.spain/index.html