Is the EU's Schengen treaty unique?

Yes, there are other Schengen-type treaties around the world? Some Schengen-like treaties in the western hemisphere.

North America 

At various times, the United States and Canada have enjoyed a functional Schengen treaty arrangement, even though it was not formalized. US citizens did not require a passport or visa, nor pay any fee to travel to or from Canada. The same was true for Canadian citizens traveling to the US. This protocol was observed for automobile and passenger rail transit, although I am uncertain about air travel.

 
I was an enthusiastic novice international traveler in the 1990's. I was eager to get as many stamps in my passport, from as many different countries as possible. On a drive from Seattle to Vancouver, I had my passport with me, although it wasn't necessary. The Canadian immigration control officer was amused at my request for a stamp of entry, and eventually dug one out.

Automobile traffic to and from Mexico and the United States did not require a visa or passport. Most border crossings that were familiar to me were via a bridge-like structure (sometimes over water, but not always). Crossing on foot usually entailed much closer inspection, and I would bring my passport just in case. Walking across the border was not necessarily done of necessity, as it was quicker and less complicated for me as an American to leave my vehicle on the El Paso side of the border, especially since I limited my visits to Ciudad Juarez.

 
Google Maps war against cartographic ignorance

Central America

El Salvador, Guatemala, Honduras, and Nicaragua signed a treaty in 2006 that allowed citizens of each nation to travel freely among the other three. The Central America-4 Border Control Agreement was applicable to travel by land, only, and required checks at borders for air travel. Citizens of Greece were also allowed to travel freely among the CA-4 countries, with the exception of Nicaragua, which required visitors from Greece to obtain a tourist card.

I do not know if the CA-4 Treaty is still in effect.  In November 2010, imprecision in Google Maps reignited a long-standing border dispute between two of the signatories, Nicaragua and Costa Rica. Hostilities escalated and war was barely averted. I wrote about it here, Google Maps: Foreign affairs and social skirmishes.