Democrocy or Republic?

I have often heard the notion that the United States of America's federal government is Democracy, yet when I was in High School Social Studies class, some 20 or so years ago, they taught me that it was a Democratic-Republic. However, according to the 1906 American Historical Review, as record by Constitution co-signer James McHenry, Benjamin Franklin clearly stated that what had been created by the U.S constitution was a Republic.

Why is this distinction so important? While in today's vocabulary the two words are almost considered synonyms, the sentiment of being a Democracy, or majority rule, is very different from the original meaning of a Republic, or to rule by law. The word "republic" comes from the Latin res publica, meaning "the public thing(s)," or "the law(s). "Democracy," on the other hand, is derived from the Greek words demos and kratein, which translates to "the people to rule." In other words, what ever the majority of the people want, or a conglomeration of such things, is what they tend to get.
So what's the problem with Democracy? Maybe this video will help.

An explanation of the various forms of government, and why America is not a democracy.

Today, instead of sticking to the constitutional restrictions, or hard set "laws" set by the constitution, we getting what the majority of our elected officals precive as the latest fad their constituents are in favor of. Instead of sticking to hard set rules, we have created a mammoth sized government that is trying to please and be all thing to all people. A true republic, would stick to it's roots, or follow the rules, such as constitutional amendments, instead of passing laws that can be easily changed and modified until they become so convoluted that nobody knows what to expect.