A lot of it depends on what tires you run, how well your car is set up, how well you drive it, and how close to the pointy end of the grid you intend to run. Another important factor is how abrasive the tracks that you're going to run on are. Some tracks are a lot harder on tires than others.
As Kirk mentioned, it also depends on which end of the car you run the tires on. As a general rule, I found on my ITB Rabbit GTI, that tires would last 2-3 times as long on the back, as they would on the front. That's a purely subjective observation, as I never ran tires only on the front or only on the rear, they got rotated through, to maximize life.
Using the MARRS series at Summit Point as an example (6 races, 5 weekends, not counting the races at other tracks). 2-mile track, 16-lap races, 2 20-min. qualifying sessions. To run all of those races in an ITB VW, I would say that you could probably get by w/ 6 tires (but probably not Hoosiers). I'd have 2 extra on hand, just in case. A key thing about tire life is getting them properly scuffed in and heat cylcled. Having 8 tires (and 8 wheels) gives you the ability to do that fairly easily.
That being said, I used to carry a few extra wheels/tires to the track. I'd usually take two to two and a half sets of drys and a set of wets. Having a 24' enclosed trailer gives you a little extra room.