There are 347 schools in NCAA Division 1. (This doesn't count "affiliate members" like RPI which are Division I in only one sport - hockey in RPI's case.)
I count 36 sports with team championships, so since 1973 there have been at most (40 x 36 = 1440) team titles on offer. In men's basketball, only 35 institutions have won titles in 74 years and I count 20 in the 40 years 1973-2012. Assuming a similar distribution in other sports (I count 14 teams in 30 years in women's basketball) would suggest 720 institutions winning titles if and only if no institution won in multiple sports; that's not a safe assumption either. Also, not all of the 36 sports have had 40 championships.
I sampled the list looking for national titles. Of the 20 programs listed under "A", only five (the Universities of Alabama, Arizona, and Arkansas, Arizona State University, and Auburn University) had won national team titles. (The University of Akron has a national title in a non-NCAA sport, archery.) This suggests that of the 347 schools, there are probably only about 87 with any team titles at all. That suggests to me that there are in the area of 260 programs with no national titles at all. I doubt the number is as high as 300, but I also doubt it is lower than 200.
The majority of the sample with any titles had several; the University of Arkansas, for example, in addition to one men's basketball title, has 40 across men's indoor and outdoor track and cross country.
If anyone wants to build a comprehensive list of title-less programs, start with the complete list of programs, then look through the sports and eliminate programs with wins. What's left is your list.