I guess it depends when you went to school.

In the 60's and 70's the prevailing thought was that the extinction was due to some sort of climate change, most likely excessive volcanic activity, which would have shot a lot of ash and dust into the air resulting in a "nuclear winter." The prime suspect for this were the large volcanic deposit in Asia (the Deccan Trapps) which appear to be about the right age (65 million years old). Scientists had witnessed how volcanic activity can seriously affect the world's climate before - for example, the year that Krakatoa erupted was the coldest on record. So it seemed logical to assume that perhaps a larger volcanic event could have killed off the dinosaurs. Luis Alvarez proposed his asteroid collision theory in the 1970's, but it really didn't gain much acceptance until data on the Iridium layer started coming through, and then further evidence of a massive impact near Cancun Mexico came forward in the 1980's. This was the "smoking gun" that convinced most (though not all) that the extinction was due to an asteroid.

Actually, my brother did a study of the geology of the area, and showed that high concentrations of sulfur that are in the area would have created sulphuric acid particles in the atmosphere that would be particularly effective at reflecting sunlight back into space, thus lowering the earth's temperature for several years. Here's an article from Time Magazine that mentions this:
A DOUBLE WHAMMY? - TIME