Basicaly everybody is used to usual data like GDP, population, administation budget. So I'm looking some original and unexpected open datasets.
I could say that I have spent hours on datasets research and the most unexpected dataset I have found till now is the last words of every inmate executed since 1984 in Texas.
You can find the portal with the data in the official page of Texas here:
I quite like
Restaurant food inspections ?
Crime reports ? Also on durham open data web site.
Your interest will mainly depends on your country or city... it will be interesting if you live in the country of the data provider...
http://data.opendatasoft.com/page/home/ for french people for example